Whew! Go easy on the colors!There are no phrasal verbs here.
It doesn't need forms the main clause.
need governs infinitives, so an infinitive follows (to be).
be can act as a linking verb to a noun or adjective, so an adjective can follow. (open)
be can also govern past participles of verbs to form passive constructions. (opened)
So either of your two sentences is possible.
It doesn't need to be open. = There is no need for it to be in the state of being open. (You can close it if you wish.)
It doesn't need to be opened. = There is no need for someone to open it. (It can remain closed if you wish.)
CJ