They're also often one and the same.
Current attacks on trans adolescent healthcare, which JKRowling is advocating for, are led by a legal team best known for challenging access to abortion. If they remove Gillick competency for trans health they will then go after birth control https://twitter.com/hlmacmillen/status/1280943070222024704

The lawyer on the case against trans healthcare is Paul Conrathe, he worked for Christian Concern/Christian Legal Centre, Evangelical lobbying group on cases including attempt to ban Jerry Springer the Musical & a man seeking an injunction to prevent his ex having an abortion.

Christian legal centre have previous on #supportingdetransitioners. They got huge media coverage for an MA student (& hypnotherapist), James Caspian, who was asked by Bath Spa university to amend his suggested research project topic on de-transitioners.

The whole debacle was a farce. I tried to find any occasion when a Masters student had sued a university after being asked to re-write a research proposal, (there weren't any). He inevitably lost, multiple times, at huge cost to himself poor chap (never ending crowdfunder below)