FWIW, as an amateur historian I did a high-level talk on the history of barbecue, especially as it relates to the grilling styles found in California (popularized as "Santa Maria BBQ"). Long story short, men were running the pits not only in the 1950s, but also the 1850s, 1750s, 1650s, etc. Why? It might have been because meat was the product of the hunt. It might have been because running a barbecue could mean many hours of hot, smoky, dirty work that often involved physically strenuous activity. For quite a lot of American history, barbecues were often conducted for large numbers of guests and may have started the day before with transporting fuel, digging a trench, pre-heating the trench overnight, processing one's pigs, mutton, poultry, beef, or what have you, making your coals and keeping the supply up throughout the cook, etc. Also, the cuts of meat used were often far larger/heavier than we're used to — the original Santa Maria Barbecue cooks used top blocks of beef and similarly large cuts, not itty bitty tri-tips.

Famed barbecue "masters" were universally men, though if everyone is being honest much of the hard work at many large barbecues (with hundreds of guests) was actually performed by black men (or Californios, or what have you depending upon the location). Large barbecues were generally tied to political efforts or organizations, festivals, and the like. During the Depression there were large government-subsidized barbecues so everyone could get some meat in their bellies and enjoy one another's company during those tough times, and there again we see men and women typically taking on disparate roles in the cooking process.

Contemporary accounts of the barbecues of years past generally have women inside doing not easier work, but different work. Making pies, side dishes, baking, etc. Even the pre-Columbian/Spanish Chumash tended to split their work pretty strictly, with women doing things like grinding acorn flour in bedrock mortars with the kids, while the men fished, hunted, gathered shellfish, etc. Contemporary drawings of various indigenous peoples show them smoking/grilling fish and iguana, but again everyone in the images are male. I confess I don't firmly know what kind of sex differences existed in the roles played in the cooking American slaves did for one another, something I really should remedy, but when it came to big gatherings the differences were apparent and as I wrote above.

I can't really speak to causality, but in terms of time scale the M-F patterns seem to substantially pre-date the 1950s.

Oh, and fun fact: the offset smoker was invented in Texas in the 1970s. That little factoid seems to blow people's minds...