Is there a mod that blocks users who sign up with a disposable email? Or that they can't log in with this email.

You can add them to your email bans as wildcards if you have a list of domains

But this is very impractical with the mass of disposable mails.
here a list with more than 7000 mails, from MyBB

Looks like they did the same thing. Wrote a script then inserted them into the bans table in mybb.

I can't write scripts, I have no idea.
I'm a PHP idiot