How does one best deal with ...

[Mako Koiwai]

... removing these obnoxious fastners? (Miata Fender Liner fastners)

The have a "phillips" head ... but there isn't any threading. You turn them and usually nothing happens. Sometimes the head pops out to make it easier to remove ... but only sometimes?

[Max Hayter]

I get a tiny flathead screwdriver and slip it under while using a regular screwdriver to turn. Turn and lift at the same time - works like a treat.

[Aaron Goldsmith]

Quarter turn counter clockwise (don't push), slip something under the rim and gently pull it out.