NTA, Was going to go with no asshole here until that last paragraph, by even beginning to think about it you’ve essentially cut ties with your current job, so if you want any chance and financial security you might HAVE to take the job.

Unless your family is going to acknowledge this fact, that regardless of if you stay or leave that you now longer have job security and if you stay it may be more likely that you’re going to be left without an income, then they’re essentially using their political beliefs to bludgeon their loved ones financially with. I’m really sorry you have to go through this OP,

I know it may seem like a difficult decision but this choice may be a good one to make, at some point your family is going to realise that because you clearly didn’t expect to firstly have the option to move, and secondly that beginning the process to move has essentially cut goodwill with your current place of employment, you’re going to have to stay regardless. Also, the fact of the matter is applying for visas take time, so it’s pretty impractical for them to basically strongarm you to uproot your entire plan because of 1 decision they disagree with, albeit an important one to both them and you.

Also, bear in mind there are tolerant pockets in even some of the most totalitarian of countries, although not the same, my dad spent the larger part of a decade working in Egypt, and as an LGBT person he was still able to find a way for me to feel safe and comfortable to visit despite its less than stellar record on LGBT rights.

Sorry for the essay, just make that move, and if your family is understanding enough of who they raised and the values you hold they’d know you are doing it with your wellbeing. Though maybe start looking for jobs back home as well. Good luck!