What a debate!!
If I'm not mistaken, the green egg gene is carried by the rooster, so if you have EE that lay green eggs that are with a green egg-hatched roo, they would be 'pure' for this swap.
Monkeyinaroundfarm's eggs should be 'pure' EE, since any pullets should lay green eggs, though I'm not sure if the roosters from that mix would carry the green egg gene? You'll have to get back with me on what the 'experts' say.
If the roos and pullets both from your mix would carry the green/blue gene, they would be considered pure for this swap.
A purebred bird is one that consistently has the same characteristics. So if you have a flock of birds that lay green/blue eggs, and the pullets hatched from this flock also lay blue/green eggs, that would be a consistent characteristic.
Frizzles and sizzles are also considered 'pure' for this swap, because they have a name. Like a labradoodle dog, they are mixed, but they are also desired. I consider them a 'designer' breed.
The reason EE's are considered pure is because no one has complained. Some EE's are mutts, but as HBuehler said, some are not. 2 pure ameraucanas that are of different colors, or not a recognized color, are not considered ameraucana. Ameraucanas must breed true. So those are considered EE's.
Hopefully, those of you that send 'pure' EEs will send those that are green or blue covered by a roo that hatched from green or blue.
This would make them 'pure' for this swap.