It sounds like there may be a market opportunity for someone to start a biological-female-exclusive sports organization. The XX-Games?
A woman owning a gun would not stop a biological male from stealing a sporting award from her by competing in the women's category claiming to be a woman, or a mob from physically attacking her for saying it was unfair.
https://www.rebelnews.com/transgender_swimmer_lia_thomas_exposed_report
Discussion
Alternatively just don't allow men to compete in women's sports by claiming to be women, it's not hard. It's easy to test objectively whether people are male or female, it's written in their DNA.
The question to me is “who’s league is it?” Someone must be the owner/operator of the league, and it’s up to them to decide what their criteria are for competition.
A successful league operator will choose those criteria which attract competitors and viewership. If the league operator chooses their criteria poorly, they should go out of business, leaving an opportunity for a competing league operator to fill the market niche.