I've found the problem, it was chat-related extension that was conflicting. I was an idiot and threw it in there to see what it did despite the person who made it saying it wouldn't work and forgot all about it. The chat for me now works perfectly fine even if I switch scenes and everything and it doesn't "un-synchronize" either.
I've also found that having the WASD keys set as the arrows, will make the chat scroll up and down while you type if using those keys in what you're typing, thus making it appear "un-synchronized". So, it may be that instead of the scene issue, because I've tried switching scenes a lot and never had the problem that you said.