this is an imprecise term i've seen used in multiple ways over a long period of time, so i should clarify what i mean. i use the term to refer to a capitalist that sees marx as providing deep insight into the operation of capitalism, and marxism as a system that can subsequently help a savvy capitalist to achieve their aims, if it is understood properly and deployed effectively. a vulgar marxist would use 1984, or the shock doctrine, as a user manual to establish deeper levels of capitalist control. the idea is that a vulgar marxist does not want to argue against marx, but to use marx' insights to strengthen capitalist domination.
fdr is often cited as the paramount vulgar marxist, in this context. in canada, pierre trudeau is often interpreted as a vulgar marxist.