Few comments...which should not be construed as arguments for or against the idea...
There is no "Sense/Check Deity Alignment" or anything of the sort. Clerics cannot sense the alignment of another person's deity. They can only ask their own deity to give them the deity's opinion of another person's deity. The answer comes in the form of a feeling that translates to one of allied, friendly, neutral, unfriendly or enemy. That's the extent of it. A cleric cannot know which deity it is, and once more, the cleric cannot know the alignment of another person's deity.
More generally speaking, alignments are OOC information, not IC. "Detect Evil" is sort of a hybrid of an IC concept and an OOC label, but that could spin into another topic. I just want to reinforce the idea that no cleric is detecting the alignment of another person's deity.
Mechanically speaking, it isn't a "widget" that allows clerics to detect the deity relation between themselves and another person. Mechanically, it's a 0-level cantrip/spell. Clerics get that at level 1. In an IC sense, it's more of a prayer or asking one's deity for his/her opinion, which is not delivered in words so much as a feeling, as I said. Speaking mechanically again, Paladins don't get cantrips until level 4.
Johnny Cash spent time in prison. OK, it was for drug-related reasons, but still...
Carry on.