I believe some differing accents WITHIN the U.S. also pronounce those names differently. Similar to how some accents pronounce "cot" and "caught" the same, and some don't.
I'm US born and raised and I say them differently...one starts with an e sound and one starts with an a sound. Do some people pronounce them as homonyms?
In my part of the state of Virginia "Aaron" and "Erin" sound pretty much the same due to the local accents. I have to admit that even though I don't have a particularly strong and pronounced Southern accent I have enough of one that when I say both names they sound very much alike unless I stress the "o" in Aaron and pronounce the name "Air-ON." Most Aarons I've known during the course of my life pronounced their names like Erin.
I had to sit here stupidly saying, "Aaron, Erin, Aaron, Erin," but I definitely pronounce both the first vowel sound and second vowel sound differently in those two names. The difference is subtle, but it's there. And one pronunciation definitely sounds like a boys' name to me and the other definitely sounds like a girls'! -- That'd be 18 years of a Seattle accent and 11 years of a NYC accent, don't know which is responsible.
Where I live, both are pronounced exactly the same. I do admit, though, when I sat here pronouncing both... I noticed the RON of Aaron and RIN of Erin were pronounced slightly different.
Boo! Erin and Aaron mos' def pronounced the same way, therefore, TIL some people do things horribly horribly wrong. Wait, knew that already.