My mum and dad first met by joining a cover band that performed songs by The Beatles (and a few other bands from the 50s - 70s) so if it weren't for cover bands I would have never even existed!
In general though, I really think that it depends a lot on the individual artist or band that is covering for them. When it comes to covers, I tend to prefer performers to be a bit creative and add their own little touches to the songs, so they are not just completely mimicking the original. To me, it's not very interesting to merely copy something when I can just listen to the original instead. I'd like them to give me a reason to appreciate their particular version so that I can enjoy both the original and the cover for their own individual qualities.
I don't mind as long as the cover is done well. Like if someone turned In My Life into some rubbish pop song sung terribly then yes I would get annoyed... like when Justin Beiber covered Let It Be THAT is the kind of thing that annoys me.
I don't get why Beatles fans are all anti-covers- if someone wants to cover a Beatles song, so be it- what's the big deal? It means they have good taste and just because there's cover versions doesn't mean that they have to be as good as the original! Obviously they're not going to be, but is that a reason to hate covers? With almost any artist (not just The Beatles) the original will almost always be better than the cover. Even with The Beatles themselves, I prefer their originals to their covers. Even if it was a great song and is being covered by a great artist, a cover often won't impress me as much as originals by that same artist- but that's no reason not to do covers. As a singer/songwriter who also enjoys covering, I don't see covers as trying to compete with the original song- it's just having fun and enjoying playing a song you like, and just because you didn't write it doesn't mean you shouldn't play it. One of my other favourite artists, Katie Melua, has done a couple of Beatles covers- I really like her version of "Lucy in the Sky with Diamonds." It's not the original, but for a cover version it's great. She ruined "Cry Baby Cry" though... but oh well, I still don't hate her for it.