I wouldn't go out in a jockstrap under completely transparent shorts, but I have some pairs of shorts which are just a little opaque, so that somebody would have to make some (just a little!) effort to see what is there.
Britain is uptight. In my local hotel steam room I wear a thong. I'm the only one who does; the other guys all wear dork shorts that usually cover to below the knee! Women usually wear a one piece swimsuit, occasionally a bikini.