Rabbi Sheserah

But actually studying Torah?
And is there a difference between innovations in thought and morality and faith?

Absolutely not. Everything you can learn is worth learning. What does it matter in what field?

At first glance, the Gemara prohibits it out of fear that we will not know how to separate the pure from the impure.

Am I not influenced by him when I study his teachings?

I don't think so, and I really don't think you'll be influenced by a lesson you hear about sexual promiscuity.

Is there no authority here for the GM?

Authority over what? I do not know of a prohibition against learning from a rabbi who has sinned. I know of various recommendations, and I also know that Sh”m learned from someone else, and Re”a from a rabbi who denies it. And I also know of the differences that the poskim wrote between their time when all the Torah was transmitted orally from the rabbi to our day when the information is found in books and the status of the rabbi is completely different.

Isn't there a higher spiritual demand expected of rabbis who claim to represent Torah knowledge?
Before discussing the content of his words (which are truly important to study for themselves and it doesn't seem likely to me that anyone would be adversely affected by them), don't we demand a more complete moral level from rabbis we want to learn from?
In my opinion, this is the demand of the Gemara when it says: “If he is like the angel of the Lord, – they should seek Torah from him”.

What should be the attitude towards the rabbi who committed the sin? Should he be publicly denounced or simply not called by honorific titles and nothing more?

Rambam, Laws of Talmud Torah, Chapter 4, Halacha 1, from the words and so on to the end of the Halacha, means that it is forbidden to learn Torah from him. I would appreciate the Rabbi's reference to this source.

A rabbi who has sinned is judged like any other person who has sinned. Of course, if you see that he has a bad influence, you should deal with it accordingly.
I assume that Maimonides' intention was to use him in practical teaching (to learn halakhic judgment from him), and not to learn Torah from him in a class as is customary today.

Does a stench impair halakhic judgment, or does it add an unknown bias and therefore one should be suspicious of his motives and not accept anything without proof?

A stench can indicate a strong influence of instincts (a sign and not necessarily a cause). I wouldn't trust the judgment of a person driven by their instincts.

Interesting. I don't feel that way (unless there is clear reason to suspect). Perhaps it could be tested empirically. That is, to collect thousands of rulings from different judges, both scorned and anointed, and to present them to distinguished rabbis who would express their opinion on the contents. I personally would be very surprised if there would be a statistical gap in favor of the anointed judges. I understand that in your hypothesis there would be such a gap?