I don't see how Baker would prevent SCOTUS from hearing Perry, but maybe I'm missing something.
Scotus is not prevented from hearing any case that is Petitioned for Certiorari.
It takes 4 Justices to grant cert., called the Rule of 4, if they can not muster the 4, then the appeal is not worth hearing for one legal reason or another, at least to them.
Note though, as the SC has stated before, a decision not to grant certiorari, is NOT in any way a decision on the merits, such as Baker was.
We have 2 distinct discretionary reviews. Baker was a decision, albiet a Summary one, as it is called.
Appeals not granted certiorari, are NOT decisions on the merits.
This is the legal difference between the 2. The SC could have denied certiorari, or as Wikipedia calls it, mandatory review (??).
Would this be binding on the lower courts, NO.
So whether they issued a Summary decision or denied certiorari, some call it the same legal conclusion. I don't.
I might be counting my eggsalads before they hatch, but I think it's a matter of when SCOTUS will hear this case, not if.
Tuna salad is better.
As I stated, you can bet your Constitutional $$ the decision, when it is handed down, will cite Baker.
My prediction, it will be dismissed due to Baker.
The SC, if it is appealed by the loosing party, will grant certiorari to uncloud the issue, this way, Baker, if simply a guideline, if you will, will be overruled or upheld, and no question will be left.