She shouldn't have done it, that much is certain, but I still think a caution is supportable. He'd been on a long time and wasn't being dealt with, and we also don't know what he was saying to the players. Male players probably wouldn't feel threatened in that situation, but there is possibly an argument to say that female players would feel more uncomfortable.
In my experience they don't have anywhere near the same level of stewarding in the professional women's game as they do in the men's. Obviously the crowds are smaller, but there also seems to be an expectation there is less likely to be any bother, understandably as the crowd are much more family orientated and there is a lot less alcohol involved. I certainly can't remember ever having a pre-match safety briefing on a WSL game, whereas there were fairly common on National League games.