I'm convinced. Where can I mention that women are very welcome?

FWIW, using "they" to refer to a specific individual of indeterminate gender is perfectly acceptable in my dialect. For instance, I could totally say "Some biker nearly ran me over today -- they weren't even wearing a helmet!". Your example of "They were a world record high-jumper" is a bit odd, but only because that sentence sounds like it comes from a biographical article or something, and it'd be pretty unusual to write a biographical article without being aware of your subject's gender.