Would it be unreasonable for a character who has taken a 1 level sorcerer dip to take Eldritch Heritage without meeting the prerequisites? I realize this is not in the RAW, but I'm curious how others would handle this and why. I'm inclined to assume they have met all prerequisites since they already have the bloodline in question, and would have no issues with them taking Improved Eldritch Heritage and Greater Eldritch Heritage to advance their bloodline powers.
No. The prerequisites are there for both game balance and fluff.
Eldritch Heritage is tremendously powerful, so it should not be easy to get.
Select one sorcerer bloodline. You must have Skill focus in the class skill that bloodline grants to a sorcerer at 1st level (for example, Heal for the celestial bloodline). This bloodline cannot be a bloodline you already have. You gain the first-level bloodline power for the selected bloodline. For purposes of using that power, treat your sorcerer level as equal to your character level – 2, even if you have levels in sorcerer. You do not gain any of the other bloodline abilities.
So, your question is:
Would it be reasonable to allow a PC in my homegame to take a feat while ignoring both the benefit and pre-requisites of the feat to advance the class features of a class he took one level in?
Now, since you seem to indicate he would be taking Eldritch Heritage for the same bloodline he has as a sorcerer, he wouldn't get a bloodline power (he already has the 1st level power from his class), so the only benefit would be that his sorcerer level would become character level -2 for this one power.
Since this is the same benefit as taking the feat without having the class the character isn't gaining anything that I can see. So I guess despite being entirely against the text of the feat, it would be okay.