Some might say that the common element for all these variants of socialism was a belief in the labor theory of value. But it may be more precise to say that the comment element was more general: namely, that workers were cheated by the reigning system. That need not commit one to the labor theory. In fact, Austrian economics contains an implicit exploitation theory, which was made explicit by Eugen von Böhm-Bawerk. As I wrote in "Austrian Exploitation Theory":
Böhm-Bawerk was merely applying the more general exploitation theory held by free-market thinkers at least back to Adam Smith: Monopolies and oligopolies (suppressed competition) harm consumers and workers through higher prices and lower wages. For Smith monopoly was essentially the result of government privilege. This largely has been the view of later Austrians, also.This should be uncontroversial. In the corporate state, government privilege restricts competition among employers in a variety of ways and -- just as important, if not more so -- forecloses or raises the cost of self-employment and other alternatives to traditional wage labor. So worker bargaining power is reduced. The difference between what workers would have made in a freed market and what they actually make represents systemic exploitation.
I'm not saying that libertarians should call themselves socialists today. That would not communicate well. But this semantic history has its value.