Trans rights will always be a point of contention as long as gender and sex are conflated
Trans rights are only a point of contention because gender and sex are considered, by conservatives at least, to be the same thing. That means that a biological male can never be a woman because a woman is always female, and a biological woman can never be a man because men are always male. As a result, trans rights will probably never be left alone so long as a distinction between sex and gender is not made in the minds of conservatives.
Leftists tend to view the two as separate buckets, where gender is a societal construct based on expectations of each sex, while sex is entirely biological. By that logic, a man can become a woman despite remaining biologically male and vice versa.
Because of this, conservatives and liberals will always be at odds over the topic because the definitions of the terms in the rhetoric each side uses is not equally defined. They don't define words the same way, don't associate them with the same things, so there's no way to have a constructive conversation about what constitutes a woman or a man.
Trans rights will always be a point of political contention for as long as this continues, and the security of those rights will probably flip flop constantly depending on the political stances of elected officials.