I don't really get how they are/were a "safe product". They certainly had mass appeal. But so did the Beatles and Stones. Where the Eagles weren't necessarily groundbreaking, they certainly were talented in every sense of the word (writing/co-writing, marketing, playing, performing).
There's a reason they still get major airplay. Countless bands could only dream of being middle of the road, if Eagles are considered the benchmark.
I honestly I can't figure out what there is to hate about the Eagles. Their personalities?
Speaking of middle of the road... I can't speak for anyone else, but despite the popularity of hate towards Nickelback, I don't really hear them much like I did early 2000s (radio, elevators, stores, whatever), and haven't for years. I can't really say I hate any bands - maybe just indifferent. But when I hear Nickelback I want to claw my eyes out. From the first song I ever heard by them, I wanted to vomit. No one told me to hate them. I had never heard of them before that. I was just listening to the radio and some new song came on that was horrible in every way, which turned out to some band called Nickelback. I just knew when I heard it that I really didn't like it. And they certainly never got any better for me.
OTOH I don't think I've ever known anyone who truly cannot stand the Eagles, apart from just being sick of hearing them. I know I can't think of anyone who said they didn't like them when they first heard them.
Off topic, but I don't really get the hate toward Coldplay, either. Not my favorite band by any means, but they had a few songs I really like.