How to get people to "like" my fb music page yet deny their friend request for my personal fb?

[some guy]

From your avatar, you appear to be quite an attractive lady (not hitting on you, just explaining the answer I'm about to give). Further to that first response, which is (I think) correct in suggesting you make a different profile for your music page, change your avatar to something which doesn't show your face clearly or "ugly" yourself down a little (ie wear something kinda dull, have a neutral expression on your face - like you're posing for a mugshot : nothing turns me off more than a lady who isn't smiling).

Or, make your avatar your guitar and your cover page your face (so people viewing your profile in search only see a guitar and not a lady).

Also, while I think about it, if you have any music on Youtube there's an app called 'Profile Song' which embeds a Youtube video to your profile and, therefore, it might also promote your work a little (assuming you're unfamiliar with the app).

Failing any of that, take it as a compliment.