It's not as simple as either side makes it out to be.
1st off, what your describing is not innovation. It is iteration. Games generally get better by doing one of 2 things. One, by coming up with new, interesting, untested idea to grow the set of possibilities in play. The other is to take existing ideas and tweak and tune them to make it something better. Both are difficult to do right, and create fantastic games. But we live in a world where innovation can seem like a distant dream. It's not so much that people think that CoD is unoriginal in and of itself, it's that so many other games reject the very important component of innovation because Call of Duty is so successful. Of course, that's a problem with the industry, not Call of Duty. Complaining about CoD for its stagnation is kind of like being forced to eat nothing but Dominos, Little Ceasers, and Pizza Hut for a month, and then walking into a mom and pop pizza shop and screaming at the owner, "I'M SICK OF FRICKEN PIZZA!".
Of course, CoD is not a stranger to innovation. If you take the original Modern Warfare, there was a lot of innovation going. I seem to remember some comments about how it was a refreshingly down to earth game that finally broke away from the over-saturated WWII shooter market. But that was 5 games ago. Multiplayer may receive tweaks and variations, but it is all variants of the same core aestetic, and easy for a person who is not hardcore into the multiplayer to not appreciate as being worth $60. The other problem is that CoD does this thing where the single player portion is great, but very short. The game can end up being judged based on that limited content. CoD succeeds because of the combination of short but sweet campaign, interesting side content like Spec Ops or Zombies, and a refinement of the multiplayer as one giant package. But take each of those individually and you have a criminally short game, the equivalent of an extra content DVD, and a tweaking that can only be appreciated by hardcore fans
Also, CoD is accessible, focusing on mass appeal. This is not bad, but it does undermine a sense of community. Its a fallacy that appealing to a larger market must take away from the smaller market. Also, that appeal comes from a very different sort of dyamic then most gamers are used to in their shooters. While a casual gamer can accept a sudden death from half way across the map as a realistic portrayal of real guns, and dismiss deaths from killstreak rewards as a part of the chaotic nature of battles, core gamers are instead reminded of taking clip after clip to the face in older shooters, where all fights are determined on the ground level, and feel like they are the victim of cheap tactics.Its the same sort of thinking that leads to older people dismissing games as a new medium. We don't like it because its not what we are used to. To enjoy CoD, you have to accept it on its terms. Casual players can do that with ease, and most core gamers can with various degrees of difficulty. But the most entrenched can't, and this could be seen as either stubbornness or personal taste.
Also, Call of Duty has a bad community because its so popular. It's inevitable. Most games are fine, but the bad experiences are more memorable. But that is a drop in the bucket. Other games have there trolls, if perhaps less blatent. Community is certainly a complaint, but really, I suspect that it is a complaint that gets tacked on after a person decides that they don't like the rest of the game.