Both are grammatically correct, but the correct answer is A. You’re talking about your opinions, so it has to be about their opinions, not about them. If you were talking about yourself (as a person), it would have to be about them.

“They don’t agree with my opinions. I don’t agree with theirs, either.”

”They don’t agree with me. I don’t agree with them, either.”

Agree on has two meanings: -1- to share the same viewpoint or opinion, or -2- to make a joint decision (perhaps a purchase contract).

-1- My friends and I agree on most things.  (=We usually have the same opinions.)

-2- The sales representative and I have agreed on a price and delivery date.  (=We made a decision about the details of a purchase.)

Agree with has one meaning, to share the same viewpoint or opinion.