Do they ask for your opinion?
Do they ask your opinion?
Is it OK to take out "for"?
We usually say "ask your opinion" when we mean "ask you what you think". We say "ask for you opinion" when we mean "ask you to give them your opinion". Therefore, "ask for" implies some sort of request for something.
For example, a reporter can keep asking a politician for his/her opinion but the politician can keep shunning the reporter. But if the politician has no problem with it, the reporter will simply ask him/her opinion.