I don’t see any legal reason that they couldn’t. If so, it would be in their State Constitution.
It’s entire a State matter, nothing to do with the Federal government. (Unless they start to collect a poll tax, or restrict voting to whites, etc.) It’s deciding how their state will assign its votes at national Party Endorsing Conventions.
But the Conventions are under the control of the Parties. They could make rules that restrict this (at least to the extent of denying recognition to the states’ delegates). I believe the National Democratic Committee already has such a policy – if any state moves their delegate selection process earlier than Iowa or New Hampshire, those delegates will not be seated at the Convention.
But that’s an internal Party matter, not a legal restriction.