Can a state make a law that deputizes individuals to sue individuals
in other states?
This question (apart from the question below that implicates federalism concerns about a sister state court process in the secondary question below) would be resolved by the constitutional limitations on personal jurisdiction and choice of law.
A state can have a law that authorizes a lawsuit for non-judicial system conduct against a non-resident of the state if it meets the requirements of "long arm jurisdiction." The most succinct description of this requirement is that the person being sued "personally availed themselves" of the laws of the state whose law authorizes the lawsuit, in a manner that would reasonably be understood to subject that person to the state's legal authority.
This could involve a lawsuit against someone outside the state arising from an incident that took place in the state. It could also involve a lawsuit against someone who took tortious action directed at a state or people in a state that caused harm, or a lawsuit arising from a business transaction that could reasonably be considered doing business in the state imposing that law.
Constitutional law requirements on "choice of law" require that the state or foreign jurisdiction whose law is applied to a question in a dispute must have some meaningful connection to the disputed issue (subject to the backdrop rule that the law of a jurisdiction other than the forum where a case is litigated is presumed to be identical to that of the law of the state where the case is being litigated if no party provides any evidence or legal authorities to the contrary).
Case law on state level qui tam litigation (which involve statutes that empower private individuals to sue someone who has wronged the government on its behalf for a share of the amount recovered for the government), the case law regarding private criminal prosecutions that are available in a handful of U.S. states, and some California consumer protection laws (which authorize suits without personal showing of actual damages in some cases when there are fraudulent advertisements) might also be relevant. So would the authority granted to bail bondsmen that is similar to law enforcement authority but limited to people authorized a person posting a bail bond for a criminal defendant who is subject to that authority.
Concretely, if the constitutionality of the Texas law was upheld<1>, Texas probably can authorize a lawsuit against a California resident who would be involved in an abortion that took place in Texas that was illegal under Texas law. And, a judgment from a Texas court in a case like that would probably be entitled to full faith and credit in California.
But, Texas probably couldn't constitutionally authorize a lawsuit against a California resident in connection with an abortion that took place in California.
There would be, of course, many edge cases with no close past precedents, where the application of constitutional jurisdiction and choice of law limitations would be far less clear.
<1> The majority opinion by five conservative justices other than the Chief Justice deciding not to stay enforcement of the law specifically limits itself to whether the proper parties were joined to the request to enjoin the statute and states "this order is not based on any
conclusion about the constitutionality of Texas’s law, and in
no way limits other procedurally proper challenges to the
Texas law, including in Texas state courts." A decision that has not been resolved on the merits. The Courts have merely declined to stay enforcement of the law pending the current litigation over the law's validity. Upholding the law on the merits would require courts to overturn existing precedents related to abortion restrictions and other legal issues.
Is there any extra legal barrier that would prevent states with
pro-choice legislatures from passing laws designed to counter the
anti-abortion deputies?
For example, California could pass a law that deputizes private
California individuals to sue people who sue abortion providers, and
could reimburse their court costs up to $10,000.
This seems to be a separate question from the question in the title. A law of this character would probably not be upheld.
Basically, it would make a state authorized legal process in one state's courts, actionable as illegal in another state.
Generally speaking, interference in another state's legal process would either violate the "dormant commerce clause", or the "full faith and credit clause", or constitutional limits on jurisdiction and choice of law, or constitutional standing limitations (even though they don't apply in the same way in state courts as in federal courts, or the "due process clause" of the 5th or 14th Amendments, or the "privileges and immunities clause." The exact legal theory isn't clear because there is really not history of litigation over this kind of legislation and you'd need to resort to vaguely analogous cases.
The effort of Texas to litigate Pennsylvania election law administration following the 2020 election was recently dismissed by the U.S. Supreme Court for lack of standing and that is suggestive of how this case might be resolved, even though it isn't strictly analogous.
It is also informed by the long standing common law rule, that could conceivably have constitutional dimensions, that litigants participating in a court process in good faith are immune from collateral litigation in another lawsuit over their conduct in the original lawsuit.
There isn't a lot of precedent one way or the other with laws having this kind of purpose, and none on a law exactly in this form. Indeed, a dissenting opinion from the U.S. Supreme Court yesterday by the Chief Justice and two of the liberal justices (with which the third liberal justice states he agrees without formally joining that opinion) stated that:
The statutory scheme before the Court is not only unusual, but
unprecedented. The legislature has imposed a prohibition on abortions
after roughly six weeks, and then essentially delegated enforcement of
that prohibition to the populace at large.
The last time there was significant litigation of laws with a similar purpose that were adjudicated was in the pre-U.S. Civil War period in abolition of slavery oriented legislation. But, the post-Civil War amendments to the U.S. Constitution and subsequent development of constitutional case law would render most precedents from that time period infirm.
