What about the view of the Bach and the Levush?

I didn’t understand. Which Bach and Levush?

The Bach says that one should not say “in whose abode is joy” when women and men are in one room.
The Levush was lenient since nowadays men and women are accustomed to being together.

Well, then you can see for yourself that this is a matter of accepted norms and not rigid Jewish law. It reminds me of what is brought in the name of the Chatam Sofer: they asked him about the order of reciting Kaddish among mourners, and he issued some ruling. They told him that the Magen Avraham says the opposite, and he answered, “each one with his own lottery” — meaning that he himself had made a lottery just as the Magen Avraham had made a lottery, because there really is no halakhic answer.

I don’t understand… the Bach (and also the Beit Shmuel) holds that this is the Jewish law, and the Levush holds that this is the Jewish law… What does “rigid Jewish law” mean?! Only when all opinions agree on the same thing?! When two halakhic decisors disagree, is that called custom? You yourself call it “issued a ruling”… (in my humble opinion, ruling means Jewish law…)

The Levush itself teaches you that these are not disagreements but practice and accepted norms. That’s why I wrote that this is not rigid Jewish law. If the Bach had lived in the Levush’s place, maybe he would have said the same as him. This is not like another halakhic dispute that doesn’t depend on place and time. Norms of modesty, by their very nature, are a function of society and place (obviously a Haredi person in a mixed setting undergoes a different experience than a modern religious person), and therefore even if one establishes Jewish law in relation to such a situation, that law reflects norms and is not something that can be learned from for a different place and time. That’s what I meant by non-rigid Jewish law, or not rigid Jewish law. For example, if there is a place where people normally walk around in shorts, then it can be permitted to pray in such shorts; and in a place where that is not the practice, then not. The result will be Jewish law, but if I am deliberating this question somewhere else, then the views of halakhic decisors from two such different contexts would not be relevant.

A. If there are women there who are not dressed modestly, is there no obligation of separation?
B. What the Chatam Sofer and the Magen Avraham ruled — was that specifically in their own places, but elsewhere they would rule differently? (Didn’t the Magen Avraham say this for all places?)
C. What does it mean (in the explanation of the Chatam Sofer) that he made a lottery?
Thank you very much for the response.

A. No more than in the street. This falls under the rule of “it is unavoidable and not intended.” Of course, dancing is different.
B-C. In the case of the Magen Avraham and the Chatam Sofer, this is not at all a question that depends on place, but a non-halakhic question. What he meant was that there is no halakhic answer to it, but the questioner expects an answer anyway (that happens a lot), so the rabbi simply makes a lottery — that is, he invents an answer just like that (something like judicial discretion, just to bring the discussion to a bottom line). But because the questioner expects a halakhic answer, the rabbi does not reveal to him that the answer is just a lottery; rather, he answers with a serious face as though it were the result of deep halakhic analysis. I was reminded of this case because it illustrates answering non-halakhic questions. It has nothing to do with conclusions for other places. Here it would be wrong to derive any conclusion from it for any place or any case. It’s just something made up (= a lottery).

Forgive me for going on about this topic. It just matters to me.
If there is a guest who, on his street and in his surroundings, people do not dress the way they would come dressed to the wedding (because his area is more modest), then for his sake do I have to make a partition, because otherwise I am causing him to stumble?

No. You are not obligated. He too falls under the category of “it is unavoidable and not intended.”