If memory serves me, statistically, most friendships are same-sex, so that vector will have a similar sex ratio.

Sure. But consider the stochastic matrix [1-p, p; p; 1-p]. It has eigenvalues of 1, an even split, and (1-2p), corresponding to the difference between male and female. This part shrinks at each step outward in friendship. It certainly has some influnce into site membership, but it does end up shrinking rather rapidly (exponentially!). Even a p of 0.1 (1/10 friends is opposite sex), would give a ratio of 55:45 after 10 rounds.

If we have a very biased join rate, this can reinforce that, but by itself it should be ignored.