Oh, the joys of being a Texan. Not only did our state pass a de-facto anti-abortion law that didn’t make it through the Supreme Court, it regularly defends laws that violate separation of church & state.
Of course, you can sue anyone for anything, but could you make a case that the state government is being reckless, imprudent, something similar, by continuing these pushes?
Governments enjoy various levels of sovereign immunity that generally forbid lawsuits like this.
So do kings. Guess who creates those kinda of laws, and whose interests they protect.
Sure you can sue. However winning then collecting is very difficult and expensive.
No. This is a non-justiciable political question. Your recourse is at the polling booth, not the courthouse.
Thought for sure the OP was going to be talking about Idaho. They also use taxpayer money to defend the unconstitutional laws they pass. They call it (of course) The Constitutional Defense Fund
The taxpayers.
Yes the legal system offers an easy end around to most Texans disagreeing with you at the ballot box. Just sue. That’s how our system of govt was always intended to work. 
Or one can choose to move to a state where the majority of the electorate more closely identifies with their views. Of course, like voting, moving may have to occur every few years…
Huh, I thought this was going to be about the brilliant lawmakers of Ohio, who passed an anti-abortion “heartbeat” bill which got vetoed by the governor, so now these dimwits are talking about overriding the veto so a bunch of taxpayer money can be wasted on fruitless legal wrangles.
Suing them would feel good but do nothing. Next election, toss the bums out.