I'm not sure the problem is truly the "mainstream" of Repbulicanism, although the bizarre fringe beliefs are being pulled in that direction. Let me explain my reasoning for those who might not be following it all the way.
I say that 106 legislators signing on to this has to be a result of fear of being "primaried", because there's no way 106 legislators could be this stupid. This lawsuit is absurd. The respectable conservatives who sometimes contribute to this board won't touch it, only the fringe. National Review won't touch it. Romney condemns it. Of those 106 legislators, an awful lot of them made it through law school. They aren't stupid, and they have legal training. They know this lawsuit has zero chance. There are a few people in Congress who are so blinded by ideology that they may as well be stupid, but most of them aren't.
However, they know that there is a hard core of the Republican electorate who demands complete party loyalty, and right now that means Trump loyalty. I don't think it's even a majority of the Republican voters. However, the majority of people don't vote in primary elections. The legislators know that if they are not loyal to Trump, Trump can tweet, "Congressman Smith is a RINO. We need better representation! Vote for Bill Trumpfan, who is a real Republican!", and a lot of people will do it. The majority of the country won't. The majority of the Republican voters probably wouldn't, but there is a chance that the majority of people who show up on a Tuesday to vote in an off year Republican primary just might, so they dare not take that chance.
As a result, the party's mainstream does get pulled to the right, and in this case, worse than that. Trump isn't just the right. He's the mindless version of it, plus a cult of personality figure, and politicians who might be reasonable in their hearts do not dare stand up to him, because they need the votes of his fans.