Yellow Power Ring says your character "has the Anti-Matter affiliation." Green Lantern Ring likewise says character has the Green Lantern affiliation.

Does this mean the character loses any other team affiliations? If I put a Yellow Power Ring on G'Nort, does he lose his Green Lantern affiliation? Or does he gain the Anti-Matter affiliation while keeping his Green Lantern affiliation?

In general, cards don't do more than they say.
Compare Green Lantern Ring to Forced Allegiance.

Green Lantern Ring
Equipment, 0
Transferable (At the start of your formation step, you may transfer this equipment to a character you control.)
Equipped character gets +2 willpower and has the Green Lantern affiliation.

Forced Allegiance
Plot Twist, 2
Choose a team affiliation from among characters you control.
Ongoing: Affiliated characters you control lose all team affiliations and gain the chosen team affiliation.


As you can see, if the effect is to make you lose your team affiliation, it will say it directly on the card.
Hope this helps!
-Anthony

Yes, that helps. Thanks!!

It's also lame that neither piece of equipment gives flight and range...

It is lame and, themmaticaly, it should but IMHO it would be unbalanced for a cost zero equipment

if it DID give flight and range it would simply be too good, without a higher cost, which would negate its usability. I think they got it just right. As is, they are VERY good cards that will be a 4-of in any willpower deck.