Oh, some of them surely have morals. They just work very hard to keep them buried and hidden out of sight. They mortally fear being thought of as narrow-minded. They desperately want to be considered trendy and progressive. Because of the libertarians' desperate need to be thought of as noble by the crass, self-indulgent, and perverted classes, Bill Clinton understands and relates to libertarians far, far better than he does social conservatives.
Such libertarians are worse than useless in the culture wars; they are absolute dead weight because they lack the courage of their convictions. Because they will not take a principled stand on moral issues ("consent" is the flabby substitute catch-all word for "morals" in their limited lexicon), they get increasingly large and more frequent truckloads of moral sewage dumped in their communities, sewage that they mewlingly and passively profess to hate.
I think there are wide variations in what libertarians believe; some of them believe that morals are important, but that government is the wrong entity to enforce them.
If the people of a town happen to believe that someone is a bad moral influence, libertarians would not object if people and businesses in the town refused to deal with that person. I suspect some libertarians would be much more willing than others to shun people they saw as being immoral, but one of the tenets of libertarianism is that the right of free association includes the right to shun others.
To be sure, society is much more mobile today than 100 years ago, so the effect of shunning is considerably reduced. Nonetheless, I suspect that if the government didn't in many cases forbid it, shunning could in many cases be as effective as legislation.