Q:

Can polyalloy (plastic) pex fittings be used with both styles of attachment rings?

Some pex fittings are made of a type of durable plastic known as polyalloy. Examples:
 
These fittings appear to be plastic equivalents of their brass counterparts.
In general is it permissible to use either the copper crimp rings OR the stainless steel cinch / pinch clamps with this type of fitting?

Notes:

This wasn't addressed in What is the advantage of PEX pinch clamp vs. crimp rings?

A:

TLDR: Yes, either type of attachment ring can be used. At least in the USA, these products have to conform to standards which make this so. Additionally, some manufacturers specifically state this is the case.

Details:
Primarily, this seems to come down to manufacturing standards.
In the USA, "PolyAlloy" fittings are governed by standard ASTM F2159 Standard Specification for Plastic Insert Fittings Utilizing a Copper Crimp Ring... which states: 

This specification establishes requirements for sulfone plastic
  insert fittings utilizing a copper crimp ring for [PEX] tubing...

Based on that alone, it would seem that these plastic fittings can only accept the copper crimp rings, not the Oetiker-style stainless steel cinch rings.
However, cinch rings are governed by ASTM F2098 Standard Specification for Stainless Steel Clamps for Securing [PEX] Tubing to Metal Insert and Plastic Insert Fittings which states

This specification covers stainless steel clamps ... that comply with F1807 or F2159, and
  cross-linked polyethylene (PEX) plastic tubing ...

Therefore by reference to F2159 it seems that the cinch clamps are effectively retconned into acceptability for use with polyalloy fittings.
For example, Everflow fittings are documented to be "Certified to ASTM F2159". And here's a marking on a Vanguard Apollo package indicating the same: 

Update: I contacted Apollo about this and they wrote:

You may use pinch rings, copper crimp rings, pro crimp rings, and
  stainless steel sleeves with any of our Poly Alloy fittings.

So at least as far as their products go, there should be no problem. And I think therefore that any of these fittings made to the same standard ought to be fine also.

