This is a pretty common type of statement that's seen frequently on internet posts and discussions, but I was curious if there was a term for it. The statement starts off with a disclaimer which is used to strengthen their argument and can even be used as a cheap way to deceive people into accepting their point of view. Here are a few examples:
"As a Clinton supporter, I completely agree that Trump is correct here."
"I don't care much for rock music, but The Beatles have some of the best albums I've ever heard."
Notice that without the first part of these statements the statements aren't as convincing.