I haven't been active in the private school sports world for a couple years, but I think the issue is that TAPPS is concerned that T-CAL is in the process of trying to start a division (especially in boys basketball) that would lead to the development of IMG Academy type all-star school/teams.
The SA Express News ran a big story (page 1 front section; two full pages inside) about St. Anthony HS, which had some run ins concerning the inducement process that led to the enrollment of several foreign basketball players at the school. The school withdrew and joined T-CAL and is a part of their elite basketball division.
My issue with these schools is that it's tough to get the mommas and poppas to support the athletic program if their kids, who may have been going to the school since PK, get shoved farther and farther down the bench in favor of new "recruits" that get either free tuition/room board or paid by shady third parties. History has shown, at least in Texas, that private schools that go that direction tend to lose students (and hence dollars) over time. When you have a school charging $6-10,000 for annual tuition and fees, losing a couple dozen students all of a sudden is a serious drain on finances.
Also, the issue that would arise to me as an Athletic Director is how do you run your other sports programs. If you focus on boys basketball, how do you run your football program, girls athletic programs, spring sports, subvarsity sports. If people won't (or now can't, in the case of TAPPS schools) schedule you, you have dozens of kids in other sports basically outta luck because one program has hurt the entire mess.
Now, the new fly in this ointment is that St. Anthony (as is Incarnate Word HS, an all-girls school still in TAPPS) is managed by the University of the Incarnate Word, a recent D1 NCAA school. There are some questions what the University can and cannot do; there seems that there would be a significant NCAA enforcement issue if future UIW athletic scholarship recruits came through these two high schools (in the case of the young man featured in this article, he's going somewhere far beyond UIW for college in the basketball food chain).
I don't know if the new TAPPS rule takes effect immedately or allows TAPPS schools who have contracted for games (such as 2-year contracts in football) to complete those agreements entered into before the rule took effect. I do know that when St. Anthony left TAPPS, TAPPS schools were permitted to cancel any contests with St. Anthony and many of them did.