The term sex hangup, sometimes also called sexual hangups, refer to our own thoughts and feelings that inhibit or prevent us from expiring our sexuality. Sex hangup is not a clinical term, but it is one that is used in both pop culture and media, and it usually has a negative connotation to it. In these contexts someone with a lot of sex hangups is seen as too uptight or less healthy than someone who has fewer sex hangups.
Of course the term is completely subjective. If I have no interest, for example, in having sex in public, is that a hangup? Is it a preference? Maybe it's just that I'm worried about getting arrested and know that my worries would get in the way of my ability to enjoy the sex. Is it my place to say I have a sex hangup, or is it okay for my partner or friends to name my position as a hangup?
One person's hangup is another person's preference, and it's worth noting that to the extent that this term is used as a negative comment, the person making the comment is likely saying a lot more about their sexual values and beliefs than they are about the person they are labeling.