Well, there are different kinds of people out there. Usually, and if possible, I try to be polite and diplomatic. Ideally, I try to change the subject to something more pleasant, or I walk away, talk to someone else.
A:
You know, anything not using React in today's world is not worth it.
Not using it is outright stupid. I have developed websites for three whole years
and I know what I am talking about.
Me:
You know, you might be right about that.
The best course of action imho is to not collide with them, because that just results in a big discussion without end, which is very taxing on your nerves and will exhaust you quickly. Use an argument-stopper, like just agreeing with them unconditionally. Chill, be cool, let them talk BS, let them make experiences and hopefully grow up one day. That's not your job to fix, though.
In your case, your job is to fix a website. My advice would be to stay focused. Don't let their arguments bother you. Create an issue overview and tell them how it has to be fixed from a legal point of view, which results in certain technical decisions. However, don't give them any choices - you are the expert. Either they agree and you land the job, or you walk away from this madness. Your health is more important and you can easily get another job with more pleasant people, which is a boost to your motivation. Motivation is important, because no one can just work like a machine.