Answer

Not only nowadays. Every single day and in every generation one should put in a tekhelet thread. This is an obligatory positive commandment (and not merely an optional/contingent one, as some mistakenly infer from the Mishnah in Menachot, "the tekhelet does not prevent the white"). It is a Torah commandment. The question is whether the identification of the new tekhelet is correct. Here I am inclined to think that it is, and at the very least we certainly have not gotten beyond doubt. A Torah-level doubt is treated stringently (although some have raised doubts regarding positive commandments, and this is not the place to elaborate). In my opinion this is even stronger than an evenly balanced doubt.
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Questioner (another):
As a follow-up to this question, as I understand it, the tekhelet thread is part of the commandment of tzitzit. But it is well known that the commandment of tzitzit is only a contingent commandment. Meaning: do you mean that every day one is obligated to wrap oneself in tzitzit with a tekhelet thread? And if not, have you then neglected a positive commandment?
 
In addition, I wanted to ask: why should we observe the commandment of tzitzit at all nowadays?
 
And additionally, in your opinion is there a prohibition against wearing tzitzit without tekhelet (only white threads)?
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Rabbi:
The commandment of tzitzit is not merely contingent. True, some later authorities (Acharonim) phrase it that way, but they are mistaken or they are conflating concepts. A contingent commandment is one that can be fulfilled but not violated. But the commandment of tzitzit can also be violated: if you wear a four-cornered garment without tzitzit, you have neglected the positive commandment of tzitzit. Therefore, the commandment of tzitzit is a conditional obligatory positive commandment (dependent on certain circumstances), not a merely contingent one.
It is true that one can simply avoid wearing a four-cornered garment, and then not put on tzitzit, and thereby violate nothing. But by the same token one can avoid eating to satiety and thereby be exempt from Birkat HaMazon, Grace after Meals. Does that mean Birkat HaMazon is merely contingent? Of course not.
 
When I said that tekhelet is an obligatory positive commandment, I meant it in the same sense as the commandment of tzitzit. When I wear a four-cornered garment, there is an obligation to put on tzitzit with white threads and with tekhelet, and if I omit either one I have neglected a positive commandment. If I did not wear a four-cornered garment at all, then of course I have not neglected this commandment.
Indeed, the Talmud states that in a time of divine anger one is punished for not wearing such a garment in order to evade the obligation of tzitzit, but Tosafot already wrote that this does not apply in a place where people do not wear such garments at all (because then the non-wearing is not to evade the commandment, but simply because it is not the accepted kind of clothing).
 
I did not understand the question about observing the commandment of tzitzit nowadays. Why should we not observe it?
 
Indeed, there is a possible prohibition here of neglecting a positive commandment (because of the doubt whether this is the correct tekhelet). It may be preferable not to wear a tzitzit garment at all. If one goes with white only, one fulfills the commandment of the white threads, but it is doubtful whether one is neglecting tekhelet. The question is whether it is preferable to fulfill one commandment while under a doubt of neglecting another obligatory commandment, or whether it is better to do neither—neither fulfill nor violate. And perhaps this would be a commandment fulfilled through a transgression, in which case you have no commandment at all.
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Questioner:
Regarding tzitzit nowadays, I meant that nowadays in any case people do not normally go around wearing four-cornered garments, so why should we make the effort to wear four-cornered garments with tzitzit? After all, there are many conditional obligatory commandments in the Torah that we do not make an effort to fulfill (for example, the redemption of a firstborn donkey). And besides, we already wrap ourselves in a tallit gadol during the Shacharit prayer, so we are in any case fulfilling the commandment of tzitzit daily—so why is there any need to continue fulfilling it during all the other hours of the day?
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Rabbi:
Actually, there is no need. It is merely a custom. Of course, one who does it gains a positive commandment, but one who does not do it has violated nothing. As I explained, even the argument of "in a time of divine anger" does not hold water in this context.
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Questioner (another):
You wrote that there is no halakhic position that exempts one from tekhelet, but it says explicitly that the white does not prevent the tekhelet and the tekhelet does not prevent the white—how much more so when there is doubt whether this is really the tekhelet.
Ofek
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Rabbi:
This is a common mistake. The fact that the tekhelet does not prevent the white does not mean that tekhelet is voluntary. Tefillin of the arm also do not prevent tefillin of the head (in that same Mishnah in Menachot). Does that mean tefillin of the head are not obligatory either? When two things do not prevent one another, that means that if you did not do one of them, you still fulfilled your obligation regarding the other. But the first one can still be an entirely obligatory requirement in its own right. Therefore
if you put on tzitzit of white only, you neglected the positive commandment of tekhelet, but that did not prevent the white, which you did fulfill. And if there is doubt whether this is the tekhelet, then the ordinary laws of doubt apply.
See details in my article here.
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Questioner:
But that is exactly the point. Since tekhelet does not prevent the white, and there is doubt about the correctness of this tekhelet, there is no obligation here, and that is precisely why this halakhah exists. After all, you cannot obligate a person in a commandment he cannot fulfill, and according to the laws of doubt he is not obligated at all, because once there is doubt about a commandment there is no obligation to fulfill it. The parable/example from tefillin distorts the issue, because we have no doubt about what tefillin are or whether the head exempts the arm, etc. The correct example/paradigm is whether there is an obligation to put on Rabbeinu Tam tefillin. And the Vilna Gaon's answer is valid here too. All the more so when there is more than one view about tekhelet, and unlike tefillin it is impossible to fulfill all the possibilities.
Ofek
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Rabbi:
Hello Ofek.
I explained the matter, and I will repeat it again.
First we have to examine the situation where there is definite tekhelet. In such a case, the fact that tekhelet does not prevent the white certainly does not mean that tekhelet is voluntary. Agreed? That is why I brought the "distorted" example from tefillin. I would be happy if you would explain to poor simple-minded people like me what exactly is distorted here (other than the interpretation you gave to my words).
So when there is doubtful tekhelet, one should fulfill it out of doubt, like any other commandment. There is not the slightest connection to the question of whether it prevents the white. This is a regular case of doubt regarding a positive commandment. Whatever you would say about a doubtful positive commandment (and I mentioned that the later authorities dispute this, though in the view of the overwhelming majority one should be stringent even with a doubtful positive commandment), you should say here as well.
The existence of several views about tekhelet is also irrelevant. The ties and wrappings, even if they are not correct, do not prevent fulfillment according to almost any view. So what has that to do with our case?
The example of Rabbeinu Tam tefillin is unrelated here, because by the same token you could also ask about Rashi tefillin. So what then? Clearly, the accepted custom does not treat this as a doubt; rather there is a ruling in accordance with Rashi, and the only question is whether to be stringent like Rabbeinu Tam. That is not a question in the ordinary laws of doubt.
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Questioner:
Thank you for the additional explanation, but you did not bring anything new that I had not already understood from the earlier remarks. First, as is known, a Torah-level doubt is treated stringently. There is doubt that this is the tekhelet, and once a person wears tzitzit with doubtful tekhelet, he enters a situation where the doubtful fulfillment nullifies the definite fulfillment—or in other words, wearing tekhelet that is not actually tekhelet causes a definite nullification of the commandment of tzitzit. Therefore in such a case, and others like it, one should not fulfill the doubtful element at the expense of the definite one, and as stated, since there is no proof that this is tekhelet, one should not put it on, and the reason is obvious. As for what you wrote regarding tefillin, that "the accepted custom does not treat this as a doubt; rather there is a ruling in accordance with Rashi, and the only question is whether to be stringent like Rabbeinu Tam…"—that is completely incorrect. There are many halakhic decisors, from the Arizal to Rabbi Ovadia of blessed memory, who determine that this is not a doubt but an obligation. So as you wrote, this is not an ordinary doubt, but not in the way you meant—and again, it is not a valid metaphor.
Ofek
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Rabbi:
I did not understand your point. Even if the tekhelet is not genuine, it has not nullified the commandment of tzitzit. And regarding tefillin, I disagree. But as I noted in response to you, I could just as well have asked about Rashi tefillin too.
Be that as it may, this entire discussion has not the slightest connection to the question of one element preventing the other, and that is what I was talking about.