Hmm, my main thought is humidity. If it's humid and/or my hands are a bit (dare I say?) sweaty, then making a sound as I lift off the fretboard can be a bit of a problem. Obviously just practising at home it's not a big problem; I either just accept that's how it is that day, or maybe just take a break, wash and dry my hands and start again.
I guess it probably helps if the skin on my fingers is good & hard through lots of practice. I confess I don't play anything like as much as I used to now, so my finger-tips have softened and the problem you describe is more prevalent. So, as ever, I think the answer to your question is maybe simply practice, practice, practice!
Lowering the action a little (if it's too high) might help to alleviate that twang as the fingers lift off the fretboard too, but I don't think that would entirely solve it. Some strings are smoother in feel than others; if you think it's the surface of the string that is contributing to the stickiness then maybe try a different brand of string. Of the strings I've tried I would think Worth Brown were maybe the smoothest in feel; I can't say I've tried anything like all kinds of string though.
Crudely, it also occurs to me that if you strum harder, the sound from your fret hand won't seem so significant! :music: