As for British politicians "hanging out with the Trump crowd":
Politicians schmooze with their counterparts in other countries. They try to build relationships. It's what they do. If someone else has a popular talking point, a politician from another country may borrow it and see how far it gets them with their own voters.
This is not some shadowy plot. It's the nature of politics, and always has been. If you don't like the arguments a politician is making to win votes, then you go out and argue back and fight the good fight, and cast your own vote to defeat them. That's democracy.
The religious right played a huge role in getting Trump re-elected.
Again, this is politics. There are many demographics who came out for Trump and swung the election his way. Some will have influence with him. Some he simply used and discarded. Only time will tell how much he appeases any of these groups. Either way, all that's America, and this is the UK. We do not have a huge demographic of Evangelical Christian voters putting pressure on Keir Starmer. You cannot seriously believe "the religious right" wields anything like the same influence in UK politics. So what are you afraid of?
If Evangelical pressure groups want to try and influence public opinion in the UK, they will struggle. The UK mindset is very different to the American one. In America, for instance, the trans issue tends to be seen as a left vs right political issue. Whereas in the UK, the majority of gender critical voices are centrist or aligned broadly with the left. We are not as sharply divided as the US. It's a very different landscape, and not one where many of these American pressure groups can easily take root.
Where do you think these groups will be successful in the UK? What do you imagine that success would look like? And how do you think it could be mitigated?
Do you have concrete concerns about these groups, or are they just a bogeyman you're going to blame every time someone has an opinion you disagree with?