The Polymorph spell does not work on "shapechangers":
The spell has no effect on a shapechanger or a creature with 0 hit points.
This answer assumes the word "shapechanger" means the specific creature subtype:
A creature is a shapechanger if they have the monster subtype (Shapechanger).
It also assumes, that any creature without that tag is not a shapechanger. That seems reasonable, but I want to back this up with any citation of game text. Aside from the specific creature subtype, the word "shapeshifter" is also being used almost interchangeable in MM:
"Solitary Shapeshifters. At some point in their long lives, metallic dragons gain the magical ability to assume the forms of humanoids and beasts"
"Reserved Shapeshifters. Older gold dragons can assume animal and humanoid forms"
"Doppelgangers are devious shapeshifters"
"Mimics are shapeshifting predators"
"perceive the original form of a shapechanger or a creature that is transformed by magic"
A Sage Advice makes things more ambiguous (emphasis mine):
A creature must be designated — with a tag or other text — as a shapechanger to count as one.
A creature might not have this particular tag although be a "shapeshifter" or "can take any shape", which might give a temptation to consider it a shapechanger in terms of Polymorph.
I'm pretty sure the Polymorph spell description assumes the exact creature subtype, but it worth clarifying. Was there any Errata, Sage Advice or an additional sourcebook that clarified this?