why not?
Their National Guard is going to Chicago.
Their citizens are allowed to sue abortion pill providers in other states.

I'm getting a little fucking sick of Texas.

In Texas, we do not have registered members of a party. In the March primary every two years anyone can vote in either party primary and after that vote, they can only vote in that party's primary. The new heavily gerrymandered districts may encourage people to cross over. Back when Houston was a one-party city back in 2000, I voted for a judge I liked who was being primaried in the GOP primary by a religious nut case and for McCain.

I hope that the Democratic party will intervene because I do not trust the GOP Texas Secretary of State

If it happened, and the governor signed it we would have to vote on that amendment. Secretary of State would not be involved as far as I can tell.

We can actually vote in one party's primary in one year then the other one the next year. The main rule is that if you vote in one party's primary, you can't vote in the other party's runoff if there is one. People flip back and forth between the two parties all the time.

Also if you are a Precinct Chair, or want to be one you have to sign a sworn statement that you will not vote in another party's primary. If you are running for a Democratic office you have some 'splainin' to do if you have ever voted in Republican primary.
I assume Republican rules are the same.

One thing about closed primaries: it will be much easier to find Democrats in our precincts because we could just pull all the registered Democrats up in our database

I don't know if they filed legislation to eliminate open primaries, but there is no way that a lawsuit can change this. You need legislation.