The cabaret style is what is more often equated with overtly sexual dancing because it's glitzy and relatively bare; but it is commonly done at weddings for the enjoyment of all.
Yes, men also do belly dance; the moves are not quite the same, they being somewhat hip-deficient. I do not thing it was the foreigners that made it a woman thing; although men dance it more seldom in the west than in the middle east.
Joanna