Question

Peace be upon you.
I was unsure whether it is permissible to vote for a secular party, or whether this involves aiding wrongdoing, "do not place a stumbling block," and shirking the obligation of mutual responsibility. I asked a certain Torah scholar about this, may he be well, and he told me incidentally that from a brief search he recently did, there does not seem to be any thorough treatment of the issue. In any case, in his opinion it seems as follows:
1. From the standpoint of "do not place a stumbling block," secular legislation itself is not a prohibition; rather, it causes those whom the law binds to stumble, and so it is a case of a stumbling block before another stumbling block, which we permit. I challenged him from the law that it is forbidden to sell a gentile a garment in which forbidden wool-linen mixture had been lost, out of concern that he might sell it to a Jew, and he answered that there the concern is that he will mislead the Jew and sell it on the assumption that it is not such a mixture; whereas a stumbling block before another stumbling block is permitted when the obstacle is known. I remarked that, seemingly, legislation resembles an inadvertent sale, since in both cases the person caused to stumble cannot avoid the obstacle. And I saw in the Talmudic Encyclopedia (entry "Do not place a stumbling block," notes 362-364) that early authorities disputed the case where one’s fellow will certainly stumble into a prohibition (and in our case, when the gate is opened for the public, it is as clear as day that there will be those who exploit the legal permission to violate Jewish law). Seemingly, since driving on the Sabbath and marriage not in accordance with the law of Moses are possible even without legislation, this is only aiding wrongdoing. And especially since, according to some halakhic decisors, secular Jews in our time have the status of apostates, regarding whom, according to the famous ruling of the Shakh, the prohibition of aiding wrongdoing does not apply. Since this is a rabbinic law, in matters of rabbinic law one may follow the lenient view.
[I also saw there (note 369 and onward) that some of our medieval authorities (the Rosh, Avodah Zarah chapter 1, sec. 14; Meiri on Avodah Zarah 14a) proved from the above law of a garment in which forbidden wool-linen mixture had been lost that with regard to a Jew there is a prohibition even of a stumbling block before another stumbling block, and blessed be God that I had intuited this correctly. Though it still requires investigation, because the distinction between a Jew and another gentile is unclear to me, since "do not place a stumbling block" is stated without qualification and applies to a gentile as well, and the explanation given in the Talmudic Encyclopedia is not fully clear to me. However, they wrote there (note 377) that some disagree and hold that even with regard to a Jew there is no prohibition of a stumbling block before another stumbling block].
Another angle that seems very open to doubt is whether it applies at all, given the tiny influence that a single vote has on the election results. I noticed in passing that this topic has been discussed on your site quite a bit, but from the utilitarian side, not the halakhic one. The objection to this is that the voter acts on the assumption that his act is beneficial, and it is somewhat like a self-imposed prohibition: he treats his act as influential, and therefore it is considered a stumbling block and forbidden.

2. From the standpoint of aiding the hands of transgressors, he told me that most halakhic decisors hold that this is forbidden specifically at the time of the transgression.

3. From the standpoint of shirking mutual responsibility, he said—though only in passing and he stated explicitly that he was not speaking from knowledge—that it is unlikely there is an obligation of mutual responsibility when the transgressor is not before us, and although it is clear that religious legislation promotes observance of the commandments, that is future-oriented and not included in the obligation of mutual responsibility. Besides that, he said there is doubt whether religious legislation in fact promotes observance of religion and Jewish law.
To this I thought to object from the concept of mutual responsibility for mutual responsibility, although it is not clear which opinion the Jewish law follows in Sotah 37b, from which it emerges that there is an obligation to ensure that there be someone who will ensure observance of Jewish law among others. Someone also pointed out to me the mutual responsibility for hidden sins, which proves that there is a concept of mutual responsibility even for a person who is not before us.
Seemingly, this point is the main weak spot in the entire lenient position.
I also remarked to him from the famous passage in Akeidat Yitzhak (Gate 20, middle of the section beginning "And in the Midrash: 'one came to sojourn'") about the institutionalization of prostitution in that community, where he wrote that an individual transgression is one thing and public authorization of transgression is another, and he poured out his wrath there like fire. He told me that certainly God's will is that the Jewish people observe Jewish law, but God's will is broader and includes additional values, so if the considerations are justified (statism, social justice, etc.) they may be taken into account.
I would be glad to hear your opinion on the matter: is it permissible to vote for a secular party, or is one obligated to vote for a party that will promote religious legislation?