How does the FAA BasicMed affect the safety pilot for somebody flying under the hood?
Short answer: the safety pilot with BasicMed must be acting as PIC, but all other regulations and considerations are the same (i.e. as if the safety pilot had a regular medical).



You have quite a lot of points in your question, but I'll try to break it down.

"[...] aren't safety pilots acting as PIC because they are required crewmembers?"

Not always. Being a required crewmember is not necessarily the same as being PIC, e.g. a typical airliner requires two pilots but only one of them is PIC. When you fly with a safety pilot there are two ways to do it:


The safety pilot acts as PIC; the pilot under the hood is a required crewmember
The pilot under the hood acts as PIC; the safety pilot is a required crewmember


As you (and the FAA FAQ) said, BasicMed only allows pilots to act as PIC, not as non-PIC required crewmembers. Therefore only scenario 1 is possible for a safety pilot with BasicMed.

Practically speaking, scenario 1 is what most people do anyway, because it allows both pilots to log PIC time; remember that acting as PIC and logging PIC time are two different things. (In scenario 2 the pilot under the hood would log PIC time but the safety pilot would log SIC time.)

"a BasicMed pilot can only be a safety pilot in VMC"

The concept of a safety pilot only applies to VMC; in IMC you're in real instrument conditions, not simulated ones. Perhaps you meant VFR, not VMC? This question (which you already found) is about acting as a safety pilot under IFR.

"Can I be a safety pilot for a non-instrument rated pilot when I have my BasicMed physical, as long as the flight is in VMC?"

Yes, if you act as PIC, as described above. And again, a safety pilot is only needed in VMC.

"Can I log PIC time while the pilot under the hood is flying?"

Yes, and this has nothing to do with BasicMed. Because simulated instrument flight requires a safety pilot (91.109), that means that if you're the safety pilot and acting as PIC, then you can log PIC time as described in 61.51(e)(iii) (emphasis mine):


  When the pilot acts [...] as pilot in command of an aircraft for which more than one pilot is
  required under the type certification of the aircraft or the
  regulations under which the flight is conducted