Sorry for getting to this thread so late. @Lily-Garden Gave a very good general response that I don't think I can top. But I did want to make a few specific comments.
Anime is its own medium. It is well-suited for certain kinds of storytelling. I mostly look for an anime to tell a compelling story in a way that uses the strengths of the medium to maximum effect. Compared to many people, I think that my expectations tend to be very forgiving when watching an anime adaptation of a beloved story. Indeed, I've noticed that people get really upset when the anime makes changes to a story. But for me, I expect the anime to make changes... otherwise what is even the point? I've read (or can read) the LN, so please tell me something than can only be expressed through a visual medium. It's a bit like when I listen to a cover of a beloved song - I will be disappointed if it is too true to the original. After all, I can go back and listen to the original at any time. Instead, I want a cover artist to reinterpret the song for me. When done well, I can re-experience the joy hearing a beloved piece of music for the first time. I feel roughly the same about anime adaptations.
I get really annoyed by the "alpha geek" tendency within niche sub-cultures to hate everything that isn't obscure or old or original. Only the original version released 40 years ago is good enough for the alpha geek (and if the original isn't 40 years old yet, he will find it inferior to something that is). This individual will find glee in pointing out every single discrepancy between the versions. In my opinion, this person is missing the forest for the trees. He is so focused on tedious minutia, that he has lost the ability to enjoy the work as a whole.
One of my favorite recent examples is "Make My Abilities Average". The story in the anime was quite different from the LN. BUT! The story itself is not meant to be all that serious, and the anime added visual gags that were very much in the spirit of the series, but that could not have been made in a printed medium. I enjoyed that adaptation (at least the first half) very much.
Another thing to consider is people who are not familiar with the source material to begin with. For example, I found Arifureta through the anime. The story itself was so strong that it somehow shone through the terrible animation. After the second episode, I couldn't wait to see what happened next and gobbled up the LNs. Indeed, it wasn't until I went back and tried to re-watch the first couple episodes that I even realized how bad it was.
Anyway, there's probably more that I could say, but I will stop there for now.