A deadhead is a freeloader, someone who gets by without contributing.

The term comes from the transportation industry, where employees of the railroad/shipping line who were riding for free on the way to their work assignments were referred to deadheads or freeloads. This practice was subject to abuse by employees taking advantage of free travel for personal use and by non-employee scammers (a more modern example would be Frank Abingale in Catch Me if You Can dressing up as a Pan Am pilot to fly free). The terms came to mean anyone who got by without contributing.

So communist "deadheadism" is wanting to be supported by the property and labor of the collective without usefully contributing in return.

Free love in the 19th century meant roughly what it meant in the 1960's and beyond, but was often associated with Utopian Socialism and Communist theory, where marriage or restrictions on sexuality were sometimes considered to be forms of oppression. Communist factions were divided on this point, and different theorists have different ways of reaching this conclusion. There were free love supporters with no interest in communism and communists who abhorred the idea of free love, but it was useful for Nast to reinforce the connection because free love advocates and practitioners were such a great boogeyman at the time.