Answer

Rabbi Raizman’s article is very interesting (as always. A fascinating Jew). I have quite a few comments, and this is not the place. Here I’ll write just one. Even someone who holds that the bridegroom’s blessings require ten because they fall under the law of a matter of sanctity, it is entirely reasonable that he means only that this is learned by a kind of analogy from a matter of sanctity (true, this is rabbinic, but the enactment is modeled on a Torah-level law), not that it itself is a matter of sanctity. It is very unlikely to view this as a matter of sanctity; rather, they learn from there that ten are required. We find something similar in the analogy between the wood of a sukkah and the Festival offering (“just as the Festival is for the Lord, so too the sukkah is for the Lord” — Beitzah 30b), where according to all the medieval and later authorities (except Rashba there), there is no sanctity in the wood of the sukkah; rather, they learned from the Festival offering only to prohibit making use of it and deriving benefit from it.
Although, at first glance, one could raise an objection from Babylonian Talmud Kiddushin 6a, which relates to betrothal as a matter of sanctity or consecration (and compares betrothing half a woman to the law of “the leg of this one shall be a burnt offering.” See Rabbi Gustman’s wonderful opening lecture in Kuntrasei Shiurim on Kiddushin). If so, perhaps there is room to say that betrothal really is a matter of sanctity. But that does not seem right, because it is clear that the comparison in the Talmud is to betrothal and not to marriage; and if so, then fundamentally the betrothal itself should have required ten as a matter of law, not only the bridegroom’s blessings (if at all).
[In parentheses I’ll add that this whole law of a matter of sanctity has struck me as puzzling for a very long time. Granted, with regard to a blessing one can say that there is a prohibition against reciting it when there are not ten present, because then it is a blessing in vain. But with Kaddish and Kedushah, what prohibition is there against saying them with fewer than ten? Is there some prohibition against saying sentences that are intrinsically true just to myself? Especially Kaddish, which has no source in the Talmud and is a custom from the Geonic period—what prohibition is there against saying it in any case? Perhaps this is considered a kind of disrespect toward the Holy One, blessed be He, and it requires further analysis. But this is the accepted practice, and I won’t go into it here, nor will I use it as an additional factor.]
I would also add that even regarding an actual matter of sanctity, I liked the distinction between “many people” and “a community,” and it seems correct to me. But I wonder why women are excluded from “community.” Perhaps that was the situation in the past, but today it has changed. This is a factual change in the status of women, and there is no reason not to take it into account in Jewish law. Halakhic decisors today are very wary of this, but it seems to me fairly clear that this is mainly because they are worried about the spirit of the times (Reform), as Rabbi Raizman also hinted at at the end of his responsum.
In sum, if I gather my comments together, in my opinion there is definitely room to be lenient and count women in the quorum (and perhaps this should be called being stringent rather than lenient). That is for several reasons (I have not included my doubts about the whole category of a matter of sanctity in general):
1. If this is not a matter of sanctity, then women are included in the ten in any case.
2. Even according to the views that it is a matter of sanctity, perhaps that is only with respect to the source of the law, not its actual definition.
3. Even if it really is a matter of sanctity, it seems that nowadays women are indeed included in the category of “community.”
4. And finally, the bridegroom’s blessings are rabbinic, and in cases of rabbinic doubt one rules leniently. True, one could discuss this differently, since in cases of doubt concerning blessings one rules stringently (lest it be a blessing in vain). But as noted, there is more than one doubt here.
And in closing I would add that perhaps in such a pressured time a welcome change in the status of women will begin, and will expand into ordinary situations as well (which is probably itself what the halakhic decisors fear, and apparently in their view that itself is a major reason to prohibit it).
I’ll just note that you should assess the character of the crowd present there, so that a commotion does not break out during the wedding ceremony. The gain may not be worth the damage.
That is my humble opinion.
May we all have only joyful occasions and good news, both personally and collectively.