JJ,
I have a self-proclaimed "follower" of Aroden who is fairly devoted to his tenets and sees him as an example to follow, but is fully aware that Aroden has been dead for over 100 years. They weren't alive when he died or anything, but his ideas of progress for the good of (human) civilization resonated strongly with them as a scholar.
So, if a secular Arodenite, with their deity unavailable for prayer, were to instead direct their prayers to Iomedae despite not keeping to her specific teachings, what would her stance on that be?
If it matters, the person in question is Lawful Neutral, and strives to act in accordance with their own views on Law and Good but is probably too flawed to properly make the grade at the moment.
She'd need them to worship her and follow her edicts and anathema, which are different than Aroden's, especially since she's good, not neutral. More to the point, since Iomedae does not allow lawful netural clerics, the character would have to change alignment. Following Aroden's tenets, by definition, means you're not following a different deity's tenets.
In short, that wouldn't work if the character wants to be a cleric. Further, if a lawful neutral character strives to act in accordance with views on Law and Good... guess what? They become lawful good. What constitutes law and good is decided by the GM, not by the players.
If you have someone who wants to be a divine caster who follows Aroden's teachings, the best options for them would be to have them play a divine sorcerer, a divine witch, or perhaps best of all, an oracle.
Or house rule how clerics rule in your game, I guess. But since you're here asking me, and I'm an expert on Golarion and NOT on your setting, I can't give you advice there.
Sorry, I missed a vital point: the character is a wizard, not a divine caster of any kind. I agree that having Iomedae grant cleric powers to an Arodenite misses both the point of Aroden's clerics running dry and the point of clerics. It's the situation of a lay person I'm having trouble figuring out.
The question I meant to ask was how comfortable Iomedae would be with a layman Arodenite (fully aware he's gone) praying to her in the modern day, keeping Aroden's tenets but directing their prayers ("Give us this day our daily bread", etc) to Iomedae, treating her as a sort of representative of the deceased. Would she be accepting? Try to (gently? sternly?) nudge them to properly assimilate into her faith, or to at least keep her tenets? Consider them presumptuous? That kind of thing. Basically, I'm just not sure to what extents this Inheritor thing goes.
(Sidenote: I feel our words aren't getting through to each other about alignment, but since it's not the main point of the question and with alignment discussions being as they are, I get the feeling that it's better I leave that topic be so as to not waste excessive amounts of time on a nonessential point.)