Disclaimer: I am not a practicing attorney, nor do I play one on TV.
It is my understanding that the following are true:
The Supreme Court has never held that religious liberty granted under the First Amendment be absolute: e.g. Reynolds v. United States, 98 U.S. 145 (1878) "[L]aws are made for the government of actions, and while they cannot interfere with mere religious belief and opinions, they may interfere with practice." Id. at 166.
While the WTS would seek relief under provision of the Sherbert test (Sherbert v. Verner, 374 U.S. 398 [1963]) i.e. "compelling state interest", the protections afforded under it (even as more widely defined under Wisconsin v. Yoder, 406 U.S. 205 [1972]), have been severely eroded since 1982. In United States v. Lee, 455 U.S. 252 (1982), the Supreme Court noted the Yoder decision, but created a significant limitation on that decision.
In Goldman v. Weinberger, 475 U.S. 503 (1986), the Court did not even apply the Yoder test; Goldman's religious claim was denied.
In Bowen v. Roy, 476 U.S. 693 (1986), very limited use was made of Yoder. Yoder 's very broad ruling in favour of religious freedom was closely qualified; note also the statement: "[T]he government is entitled to wide latitude" (Roy at 707).
Another significant departure from Yoder is illustrated by Lyng v. Northwest Indian Cemetery Protective Ass'n., 485 U.S. 439 (1988). This decision indicated that the state need not prove a "compelling state interest" (Sherbert) to justify its actions.
The decision in Employment Div., Dep't of Human Resources of Oregon v. Smith, 494 U.S. 872 (1990) likewise refused to apply the Sherbert test.
In Minnesota v. Hershberger, 110 U.S. 1918 (1990)(mem), the U.S. Supreme Court vacated the Minnesota Supreme Court judgement in State v. Hershberger, 444 N.W.2d 282 (1989), and remanded the case for further consideration in light of Smith.
Note that when the Minnesota Supreme Court supported the contention of the Schwartzentruber Amish Church in the post-Smith decision in State v. Hershberger (Hershberger II), 462 N.W.2d 393 (Minn. 1990), they simply avoided the limitations imposed by Smith by having recourse to the broad provision "liberty of conscience" found in the Minnesota Constitution.