The issue is modesty with respect to swimsuits. And the idea of young ladies experiencing "razor burn" when they hit the water in front of crowds of people hardly seems in keeping with the concept of modesty. Pope Pius XI issued some letters on the topic, and here are quotes:
Our Most Holy Father Pope Pius XI has never ceased to inculcate, both verbally and by his writings, the words of St. Paul (1 Tim. xi,9-10), namely, “Women ... adorning themselves with modesty and sobriety ... and professing godliness with good works.”[ellipsis in the original, not by me]So girls should be "fully and modestly dressed" even if they are on a swim team. And if Williamson is a nut (on this issue at least), then so was Pope Pius XI and virtually every bishop in the world at that time (within our parents' lifetimes).Very often, when occasion arose, the same Supreme Pontiff condemned emphatically the immodest fashion of dress adopted by Catholic women and girls -- which fashion not only offends the dignity of women and against her adornment, but conduces to the temporal ruin of the women and girls, and, what is still worse, to their eternal ruin, miserably dragging down others in their fall. It is not surprising, therefore, that all Bishops and other ordinaries, as is the duty of ministers of Christ, should in their own dioceses have unanimously opposed their depraved licentiousness and promiscuity of manners, often bearing with fortitude the derision and mockery leveled against them for this cause. [Sound like this thread?]
Let parents keep their daughters away from public gymnastic games and contests; but if their daughters are compelled to attend such exhibitions, let them see that they are fully and modestly dressed. Let them never permit their daughters to don immodest garb.
It is desirable that pious organizations of women be founded, which by their counsel, example and propaganda should combat the wearing of apparel unsuited to Christian modesty, and should promote purity of customs and modesty of dress.