The Supreme Court sided with abortion opponents on Tuesday over abortion rights supporters in an important case centered on “crisis pregnancy centers.”

The Court’s five conservative justices ruled that a California law that requires those centers — which do not provide abortions and often oppose it on religious grounds — to inform their patients that free or low-cost abortions would be available to them elsewhere likely violates the centers’ First Amendment rights. The law also requires centers that do not have a state medical license to disclose that fact, which the court also ruled was likely a violation of their constitutional protections.

The decision, written by Justice Clarence Thomas, sent the case back down to the lower courts for further proceedings. The four liberal justices dissented from the Court’s ruling, led by Justice Stephen Breyer.

Thomas wrote that the California law placed an undue burden on the centers’ free speech rights and that the law was not protected by Court precedents that do allow states to set some disclosure requirements for factual, non-controversial information.

“California’s notice requires covered clinics to disclose information about state-sponsored services — including abortion, hardly an ‘uncontroversial’ topic,” Thomas wrote in his ruling.

There is one interesting byproduct of the Court’s decision, though. Republican-led states have increasingly set strict requirements for what doctors must tell a woman before they perform an abortion. Those state laws have been challenged but upheld over the question of whether they restrict a woman’s right to abortion.

Now, however, it is possible that those laws could be challenged on a First Amendment basis, arguing that such requirements violate the doctors’ free speech rights. As Eric Citron, a Harvard Law School lecturer who has clerked for two Supreme Court justices, wrote on SCOTUSblog after the ruling:

One interesting dynamic in this case is that many states have laws telling abortion providers what they need to say to women seeking abortions. Those laws have been challenged as undue burdens on the right to obtain an abortion — and, as Breyer points out, have been upheld since Casey. But they haven’t been challenged under the kind of First Amendment theory developed here. In the long run, the ruling here may limit states’ ability to force doctors to provide certain kinds of information.

The full court decision is below.