Registering your political party is a state thing, not federal. Nor does every state require it. My state, Texas, does not.
You can see all the information asked for when registering to vote here:
You can see all the information asked for when registering to vote here:
I think you're reading too much into this one. The fact that not every state asks should also point to a lack of any grand conspiriacy here.
"There are two ballots here which one am I interested in again? Better ask the State which one I registered for.." Seems like a stretch.