To cut a very long story short, I have a player who is a half-drow first worlder summoner. As such her eidolon has the "Fey" type. She is wanting to deliberately infect the eidolon with the blight in Fangwood (where she operates). Technically, I think the blighted fey template can be added to any Fey. As such, the rules as written would seem to allow this to occur. Of course it will tie her eidolon to the blighted part of Fangwood (I assume) but can anyone see any rules based reason why I should not allow this. The summoner character is a follower of Cyth-V'sug.
Mostly, allowing templates is a balance issue not a rules issue. Summoners are already strong without freebie templates on top, so defaulting to no is not unreasonable.
I'm assuming you'd rather not say no outright.
You can balance it in a couple of ways. Two suggestions (technically one from two different directions).
1) the template interferes with the eidolons connection and reduces the number of evolution points available.
2) Emulate the template by buying the appropriate abilities with evolution points.
Allowing the player to bypass one of the major balancing aspects of First World Summoner (that of the fey type eidolon, significantly reducing the eidolons combat capability) for free is inherently a bad idea, balance wise. By comparison, to become roughly equivalent to a full fiend or celestial, a Summoner must spend roughly 12 evolution points: 7 for Celestial/Fiendish appearance, 5 for DR 10/alignment, and 1 for Magic Attacks.