Since others have answered the first part of this post very well, I thought as a previous student I'd try to answer some of your worries!
SOAS is famously political, but it's something you have to
choose to become involved with. It's not a mandatory part of uni culture and I personally wasn't politically active outside of my personal life as a student. As long as you don't cross major picket lines (during lecturer strikes, for example), there's no expectation to be going on marches every weekend or anything like that. It's more that if you
do want to do that, it's very easy to get involved with!
There's a whole debate about whether cancel culture exists and, to be honest, if you're a student with a limited/no public following I'm not sure how 'cancel culture' would actually work in practice in a uni setting. Unless you've done something so horrendous it warrants being kicked out. I found that for the most part there's a healthy approach to debate at SOAS and there's such a variety of people that you're always bound to get a variety of opinions too. Being an avid promoter of imperialism or worshipping far-right politicians won't make you the most loved student, but that's true at most UK unis. Most people come to SOAS because they agree with its core principles and approach to teaching -- if that's the case for you and you're a generally decent person, you don't have anything to worry about.
And finally, on anti-semitism. I think this accusation mainly comes from those outside of SOAS who don't understand what the uni actually stands for. Being an inherently anti-colonial uni, you're going to be taught post-colonial theory -- part of this includes thinking critically about Zionism and the state of Israel, as you'd expect. People often conflate anti-Zionism with anti-semitism when they're really very different topics. But, since there are sensitivities around the topic, it's always taught in a thoughtful and measured way.
A big driving force behind being anti-colonial is wanting to protect oppressed groups and challenge discrimination. This includes discrimination against Jewish people. While being a SOAS student/employee doesn't suddenly wipe away all the prejudices and preconceived ideas you might have about people, I don't get the impression it's a widespread or systemic issue within the uni. Then again, if you are Jewish yourself and concerned about prejudice at the uni, it may be worth reaching out to SOAS or current students to hear their experiences. The same goes for any other uni you apply to.
I would also like to make the point that outside of academic circles, SOAS can be quite polarising which is why I think you're coming across these rumours. A small (but frustratingly dedicated) section of traditional media has historically liked to write sensationalist articles about the uni because they see it as 'too woke' or 'too sensitive', or that SOAS students are all 'snowflakes'. When you actually get into the crux of what they're writing about, it's usually inaccurate of heavily overblown. I'd recommend seeking out past students' experiences as much as possible rather than relying on what non-SOASians think about it. That's not because SOASians are going to have 100% positive reviews -- far from it, and I actually think there are much more pressing issues at SOAS you'd need to consider than what you've mentioned above. Past students would definitely tell you all about that! So get chatting with past students and see how you feel
Hope that's helpful and do let me know if you have any further queries!