My assumption was that only magicians that can astrally project could go to the metaplanes, but I noticed that the rules say only initiates can travel to the metaplanes. Does that mean an initiated adept or mystic adept can travel to the metaplanes?

To travel to the astral- and metaplanes, one has to be able to astrally project. Only magicians can do that, not mystic adepts or adepts. If some entity opens an astral rift, then anyone could pass through, including mundanes.

The drug Red Orchid seemingly allows metaplanar access too.

Adepts where clearly intended for astral combat (Killing hands and Critical Strike). If The first adept power in the core rules book is Astral perception. If that doesn't let you project as well then how do adepts do astral combat?

The same way any dualed natured being does.

To astrally perceive is automatically to become dual-natured: active on the astral and physical plane simultaneously. To astrally project is to be active on the astral plane but completely passive on the physical.