I agree "how" isn't necessary but it's also fine. "How do your parents like pop music?" is equivalent to "What do your parents think of pop music?"
How have you been? It's been quite a while since I caught up with you.
I notice that you used a conjunction of contrast "But" in your sentence. Therefore, I infer that your parents do not like pop music.
Since both subjects (mom and dad) DO NOT like something, it's a double negative. We can use "neither" with "nor" to convey this meaning.
Answer: Neither my dad nor my mum likes it.
If I may comment, we can rewrite the question to be more grammatically correct.
Question: Alice, do your parents like pop music?
*There is no necessity for "how" as we are not asking the way something is done.
Hope this helps.