Can I omit the comma in this sentence?

Yes, but your sentence means "I hate politics, but that's not why I'm not running for office."

If you say, "Because I hate politics, I'm not running for office." then you mean that your hatred of politics has stopped you from seeking office.

Thank you.

I am not running for office because I hate politics.

This is strictly speaking ambiguous as to whether the because phrase is inside or outside the scope of not. If it’s outside, it gives the reason for your not running for office. If it’s inside, there is an implicature that you are running for office, though not because you hate politics (which may or may not

Touché.