How to disable the activation mail that users get post signing up for the community?
I Guess you’re referring to verification email. That cannot be turned off due to security reasons. You can however skip the email if you enable social login.
You would need to spend a lot of time in the code and write a plugin which bypasses all the important security checks required by the email validation process; and then mark the user as “validated” (as if the email validation happened).
Of course it is possible (it is software, everything is possible); but you will need to write your own plugin to do so.
I also doubt any professional plugin developer here would want to write such a plugin which breaks the core Discourse security feature of validating emails as part of the signup process.
Best of luck …