Your resident lawyer Kelsey here. I am going to try my best to explain the Supreme Court's order in the Texas case, subject to revision when I've had more sleep.
First, it helps to understand what typically happens in abortion cases. A pro-life law is enacted, abortion industry interests sue, and the lower (district and circuit) federal courts enjoin (block) enforcement of the law while it works its way through the system. The Supreme Court does not get involved in the proceedings until much later, if ever.
You can think of this pattern as creating two types of precedent. (1) The Supreme Court declines to get involved in abortion cases early on, letting lower courts run the show. Let's call that the "procedural precedent." (2) Plaintiffs get to keep killing unborn babies in abortions without regard to the law while the case is ongoing. Let's call that the "substantive precedent."
What makes the Texas case different is that the lower courts did NOT enjoin the law. The reasons for that are complicated but have to do with the unique citizen-led enforcement mechanism. So the procedural and substantive precedents counseled different results.
Five Justices went with the procedural precedent, basically saying that it's too early for the Supreme Court to get involved. They wrote that this doesn't mean they are declaring the law constitutional or not; they are simply letting the lower courts handle it.
By contrast, the four Justices in the minority, who took the substantive route, wrote angry opinions decrying the impact on women's so-called "right" to abortion, plainly rejecting Texas's argument that babies in the womb have a right to life. Those four Justices have made their bias plain: they will never vote to correct the Court's mistake in Roe.
The ultimate fate of the Texas law remains unclear. But for now, about a hundred babies a day are getting a reprieve.
To help, donate to a Texas pregnancy resource center! We especially love Abide Women's Health Services.