Not everyone is against this because they are anti-trans. I am 100 percent in favor of women's rights, trans rights and the rights of every person. Those rights are immutable.
But I agree with the others that it is unfair for trans athletes to compete in women's sports in some situations. Joining a team is not an inherent right. Trans athletes have a right to equal training, equal coaching, and the opportunity to compete at an appropriate level. If a trans athlete has an unfair advantage, that is not an appropriate level. Girls have a right to compete against other girls, trans do not necessarily have a right to compete against girls.
If trans athletes want to compete in women's sports, they should have to qualify by proving that they do not have a biological advantage, mostly through hormones. Women athletes currently take tests to show they don't have a hormonal advantage, so trans people can also do that. If they qualify according to the guidelines, great, they should play. But what we are talking about here are those who do have an advantage and would make the sport unfair.
For individual sports, it is easy: let them compete with the gender they choose, but have two first place awards, one for trans and one for women. Team sports are much harder, because there is often no alternative to playing on a team. But this is common for girls who want to compete in wrestling or football, they can't find a girls team to play on. Many states are now starting girls wrestling leagues, because there is enough interest. But there will rarely be enough participants to start a trans league, especially at the local level. So if a trans athlete wants to compete on a team, they may have to find a different league or compete against boys teams. They still have the same rights, they just might have to go to a different team to do it.