This petition uses an incredibly niche issue (trans participation in professional and collegiate sports) to enact highly discriminatory policies that will affect not only all trans women, but all women who do not meet whatever arbitrary standards for femininity that are set forth. It's a complete farce designed to alienate trans women and put them in harm's way. The sentiment behind barring trans women from restrooms, locker rooms, changing rooms, etc., is no different than the lesbophobia of decades past.
Athletic regulatory bodies are perfectly capable of setting appropriate restrictions on trans athletes on a case by case basis, should the need arise. This is not the job of the Commonwealth of Virginia.