There are plenty of leftists who also disparage hooking-up. Hooking-up is a hedonistic practice. Some leftists are hedonists, but not all.
If we want to discourage hooking-up, we need to discourage hedonism, which is something that religious conservatives, feminists, communitarian leftists, etc. have agreed on for quite some time.
Most leftists who are opposed to hooking-up are not in agreement with social conservatives with regard to premarital sex, however. If social conservatives demand that everyone work to abolish all forms of premarital and extramarital sex, then they won't get very far. If, however, they accept the less-than-perfect world of committed long-term unwedded relationships then we can work our way back toward a more healthy culture.
Hooking-up is also not a relativist notion. If anything, those people who believe that hooking-up is good for them believe that it is good for everyone. They are probably more absolutist about their opinion of the benefits of hooking-up than lots of people claiming to be religious are of the benefits of their respective ways of life.
If those who hooked-up were true relativists then they wouldn't mind it if other people chose not to hook-up, but they seem to be upset by this. They seem to think there is something wrong with those people that don't hook-up. Why would they think that? If they are relativists then they must believe that people should be able to do whatever they can get away with, or choose not to do whatever they don't want to.
The good news is that it is easier to have an argument with absolutists who have the wrong opinion, than with relativists who have no opinion. It can be shown that hooking-up is by-and-large bad for society as a whole and the individuals that engage in it.
There is hope especially since most people (left, right, or center) when confronted with the evidence will absolutely agree that hooking-up is wrong for everyone.
If however, they accept the less-than-perfect world of committed long-term unwedded relationships then we can work our way back toward a more healthy culture.
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No, I don’t think so. Shacking up is shacking up.