It seemed like a sensible advertising strategy. When a company discovered that women accounted for less than one-third of the purchases of its products, it shifted direction to appeal more directly to them.

But when the company is the largest condom seller in America, at a time of heightened divisiveness regarding reproductive rights and women’s health, the situation can get a little more complicated.

That is not stopping Church & Dwight Company, the makers of Trojan condoms, from unveiling a campaign on Monday that it considers the most ambitious in the brand’s history. It includes 30-second commercials that will air during prime time on CBS and NBC — a first for Trojan — as well as on networks like MTV, VH1, Bravo and Comedy Central. In early June, Trojan will be featured at the top of YouTube for 24 hours.

The campaign introduces a new product, XOXO, that is basically a typical condom. But it comes in more gender-neutral purple packaging and includes a carrying case that could slip easily (and discreetly) into a purse.