It is certainly the end of medical privacy in the US, but it may even be the end of the Supremacy Clause, which gives the federal government the ability to pass laws that override state laws.
It's difficult to overstate how much of a threat this law is to the US Constitution.
https://www.texasmonthly.com/news-politics/meet-the-legal-st...
Edit to add because I guess it wasn't obvious enough: The strategy would force the Supreme Court to quickly strike down both laws.
Now, I am not of the opinion that something has to be explicitly protected in the constitution for it to be a right. I prefer to assume a limited view of what behavior government has the authority to limit. However, if something is not explicitly protected in the constitution, then it is at least up for debate.
There's procedural implications for this distinction as well: the Supreme Court can overturn its prior precedent (as Brown v. Board of Education overturned Plessy v. Ferguson). But the Supreme Court cannot overturn the text of the Constitution itself. Only an amendment by Congress can do that.
EDIT: Just to clarify, that procedural distinction means that the Supreme Court could uphold the Texas law while overturning a similar law restricting gun ownership without contradiction.
Aside from some archaic language, the second amendment is actually fairly clear. It is clearly talking about guns, and the phrase "shall not be infringed" is fairly strong, clear language.
On the other hand, the 14th amendment say nothing about abortion, and there's no reason to suggest the authors of that amendment had abortion in mind when they wrote it.
That does not mean that such a right does not exist, or that it needs to be explicitly mentioned in the Constitution to receive protection, but any judge who wants to assert that such a right exists is going to have to do a lot more work than one who wants to assert the existence of an individual right to own guns, even "assault weapons" (which is a largely nonsense category anyway).
Instead, this is a way to get around constitutionality since it's not the government who is violating the constitution. Never mind all of other constitutional bits about due process that are being horribly trampled on (such as allowing people to sue without standing...).