Texas has had separate systems for a long time; in the early 2000's the state legislature passed a bill [Texas SB 524 allowing the 2 largest private school to be admitted to the public school org. As of today, any private school willing to have their enrollment doubled and then multiplied by 1.8 can be admitted to the public school org.
TAPPS [the private school org] members cannot exceed 725 students
Two points to make...
1) The UIL was created by the University of Texas (hence the University Interscholastic League), which was first started for debate, and then other non-athletic competitions. It just works for basically any interscholastic competition so well. Because of this setup, it has and always was just for the public schools of Texas. TAPPS was created by the parochial schools and basically mimics the exact rules. And if you want to get technical, there is/was the PVIL (Prairie View Interscholastic League) which was for segregated schools, that also basically followed the UIL setup before desegregation either closed or consolidated black schools (some still exist but are desegregated, obviously).
2) The lawsuit was that two extremely large schools: Strake Jesuit and Dallas Jesuit, were too large for TAPPS and they were essentially removed from being able to compete. Since TAPPS in Texas is mostly very small private schools. Texas doesn't have the behemoth private schools that major cities in the Northeast have. So, in lieu of some forced Act 72 like PA (where the PIAA was forced by law to admit private schools), the UIL came to the solution that the UIL will accept ANY private high school that is not eligible for admission to any of the other non-public associations (TAPPS, TCAL, TCAF, TAIAO, SBC, etc). This basically singled out just Strake Jesuit and Dallas Jesuit. Since every other private school are eligible to join one of those other associations.
That doubling enrollment, etc is because those two schools are male-only, while the UIL uses 9-12 ALL enrollment for classifications. They don't count male or female, and don't count just 3 of the 4 years for a two year cycle. And they also don't use enrollment. They pick one day, and literally count every student in attendance at the school that day. If they're home sick, etc, then they're not counted. Even if they're technically enrolled at the school. So, to get to a male/female equivalent of an all-male school, they just double the enrollment.
Also, if one of the private schools eligible to join UIL are ever caught recruiting, they're permanently banned for the UIL. So there's huge incentive NOT to recruit or even to appear to recruit.