As long as you're fine with excluding people who were born with the physical characteristics historically associated with the word "woman" from all sports, that will work. I don't think that can be the woke position, though.
Women's sports are generally a carve-out. Women can't compete with men in most sports. Because of that, I don't think that women should be excluded from men's sports. "Men's sports" are just sports, and shouldn't be restrictive. Women's sports are a subset of sports where men have been excluded in order to give women a chance. If a woman is good enough to compete in "men's sports" she should (if she wants.) The opposite is not true. This is not a symmetrical situation. If transwomen are allowed to compete in women's sports, they will dominate women's sports.
Women's sports are generally a carve-out. Women can't compete with men in most sports. Because of that, I don't think that women should be excluded from men's sports. "Men's sports" are just sports, and shouldn't be restrictive. Women's sports are a subset of sports where men have been excluded in order to give women a chance. If a woman is good enough to compete in "men's sports" she should (if she wants.) The opposite is not true. This is not a symmetrical situation. If transwomen are allowed to compete in women's sports, they will dominate women's sports.