Much as I would love this and searching really is ridiculously impossible for purebred themes, to the point I have never successfully located one -.- Krin has pretty soundly rejected this as too hard to code.

So my proposal is a bit of a searching workaround: when geneology gets in the game (goodness Krin, I sure hope that day is soon here. This is still the only pet site I've ever played where breeding was possible without that feature being in before anyone could play and I've played pet games that didn't even have an artist hired yet! XD), add to search ability to search for these parameters: Tagged, yes. Has offspring up for breeding? Yes. If the game can keep track of the offsprings existence, it shouldn't be that hard for the game to take note of a second generation being up for breeding?

This wouldn't assure it was purebred, just that one of its parents were tagged and it is up for breeding. However this would likely get you on the trail of someone who breeds X themed, and if implemented I'm sure those who do breed themes would be sure to put their second generations up for breed as a way of advertising sort of 'Hey check my stables, I breed this theme!'

I did actually make a suggestion for how to solve this issue that would allow for easy searching, be retroactive (as long as users were so inclined), and help support the site financially. You can read about it here as well as Krinadon's response.