The Attorney General of Texas filed a lawsuit claiming the results of election in four other states were invalid. If that isn't rejection of the constitution and democracy I don't know what is.
Texas likes to pass a whole bunch of stuff that they know will be struck down by the courts. It is purely for political brownie points, there is no real expectation that these things go anywhere.
In this specific case the Texas Attorney General is being investigated by the FBI and hoping to court favor with Trump for a pardon.
They had a dispute, and filed a court case, which was dismissed. What’s undemocratic about that? If they ignored the court verdict, that would be rejection of constitution and of republican system of government, sure. However, addressing legal and constitutional complaints through justice system is as constitutional and small-r republican as one can get.
It would be perfectly legal, for example, if a bunch of prominent Democrats got together and filed a lawsuit with the Supreme Court demanding that a bunch of prominent Republicans be arrested, tried, and executed for treason. It would be thrown out immediately, for a number of good reasons. But wouldn't that be... disturbing? I don't want to live in a country where prominent political leaders ask for such things, even if they're fairly sure that they'll be told "no".
In this specific case the Texas Attorney General is being investigated by the FBI and hoping to court favor with Trump for a pardon.