Is it legal for Texas to secede?

Yes. There is no federal law that makes it illegal, no statute that forbids it, and no Supreme Court ruling that closes the door on the law alone. What you are really being told when someone says "it's illegal" is a political opinion dressed up to sound like a legal fact.

Look for the law, and you will not find one

The simplest test is to ask the person who says it is illegal to point to the law. There is no clause in the U.S. Constitution that prohibits a state from leaving the union. There is no act of Congress that does it. Article I, Section 10 lists what states cannot do, in detail, and a state leaving is not on the list. When a thing is genuinely forbidden, there is a text that forbids it. Here there is none.

Silence plus the Tenth Amendment equals reserved power

The federal government has only the powers the Constitution grants it. The Tenth Amendment makes the rest explicit: whatever is "not delegated to the United States" and not "prohibited by it to the States" is "reserved to the States respectively, or to the people." No power to stop a state from leaving was ever delegated. So the question of staying or going was left exactly where it started, with the people of the state. A power Washington was never given is not a power it can use.

"Texas v. White made it illegal" does not survive contact

The one case people reach for is Texas v. White (1869), and it does not do the work they need. It was a lawsuit over bonds. Its sweeping language about a permanent union was dictum, not a binding holding, and the actual rule the case decided was overruled in Morgan v. United States (1885). On top of that, the opinion itself says the union can end "through consent of the States." A ruling that concedes a lawful exit is a strange thing to cite as proof there is none.

A war did not change the text

The final fallback is "the Civil War settled it." A war settles who had the stronger army. It does not rewrite the Constitution, and no clause was added after 1865 forbidding a state to leave. It is also worth being clear that what is proposed now bears no resemblance to 1861. That was tied to slavery and carried out by conventions. This is a peaceful, lawful vote of every eligible Texan, of every race and background, to secure their own freedom. The two could not be more different.

Texas law puts the decision with the people

What the Constitution leaves open, the Texas Constitution answers directly. Article 1, Section 2 reserves to the people of Texas "at all times the inalienable right to alter, reform or abolish their government." That right is exercised the lawful way, through a referendum the Legislature places on the ballot. Independence is not a loophole. It is a right, exercised at the polls.

The bottom line

It is legal. The opposition has a talking point, not a statute. There is no law against Texas independence, only politicians who would rather Texans never got to vote on it.