yes, it has to be "be/get involved". It's most unwise (for somebody) to get involved in ... Somebody is the logical subject for the word "involve". You should use its passive form.

Thank you CJ Hepp for the comment. Yes you are right, the sentence looks like one of those lines in Pride and Prejudice. :) Usually I would focus only on the grammar and not the style. Thank you so much for point that out. It is good to know!! :D

Yes, it has to be: "It's most unwise to get involved in a quarrel between a man and his wife." or you could say, "It's most unwise to involve yourself in a quarrel between a man and his wife." As a side note, to a common American like myself, both of these sentences sound like a proverb you would get from a fortune cookie or read in a Jane Austen novel. Even "It's most unwise to interfere in a quarrel between a man and his wife," sounds a little pretentious (to an American). We would probably say "It's very unwise to interfere in a quarrel/fight between a man and his wife," or maybe, "It's a bad idea to interfere in a lover's quarrel/spat."