That headline is the gist of this story from the Austin Statesman, even though it says the law is to "strip away transgender marriage rights." The law, as the Statesman describes it would explicitly allow certain marriages involving transgender people while prohibiting others.
I've posted before about Texas's complicated situation regarding trans people and marriage because of its recently passed law that says that gender on a birth certificate can be over-ridden by a court order, something that some counties are recognizing while others aren't. The law proposed by the Texas Republicans would repeal that law (which they says was accidentally signed into law by Governor Rick Perry two years ago... riiiiiiight) and make marriage only about matching up two birth certificates.
That would mean that marriages like those between Sabrina Hill and Therese Bur, one cis woman and one woman who was born with ambiguous sex characteristics, assigned male on her birth certificate, and then changed her paperwork in her 20's, could be legally married in Texas. To most people, that would be a lesbian marriage. But here's how the Republicans describe why that marriage should be allowed: