I think 「〜[好]{ず}き」 is a common expression in Japan these days.
If someone likes anime very much, s/he is 「アニメ[好]{ず}き」. The usage example is
http://news.mynavi.jp/articles/2015/06/21/ibayashi/
If someone likes manga very much, s/he is 「マンガ[好]{ず}き」. The usage example is
https://www.booklista.co.jp/feature/harajyuku/
Edit:
アニメ[好]{ず}き does not mean exactly the same as アニメオタク. アニメ好き represents a person who really likes アニメ. So, all アニメオタク are some kinds of アニメ好き, but some アニメ好き are not オタク or オタク-level.
〜[好]{ず}き has a broader meaning, so it's used not to precisely categorize people as オタク, ファン etc, or not to judge people's passion and knowledge levels. The word expresses a simple fact that the person is who likes it very much, no more no less. I think that's why 〜好き is preferred in everyday conversation in many cases.
Maybe, Twitter is not a perfect example for everyday conversation, but for a sort of reference,
https://goo.gl/DzCYGm
By the way, if アニメ好き is read 「アニメすき」, it means 「アニメが[好]{す}き」 or 「アニメが[好]{す}きな」. What I'm explaining here is 「アニメずき」 which is a compound noun. Tweet examples contain both types.
Some people really hate being categorized as オタク, like this questioner's friend.
http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q14107008004
So in this kind of case, 「〜[好]{ず}き」 is appropriate to use, even though the person's passion and knowledge are オタク-level actually.
The border between オタク and non-オタク is unclear in many situations, and オタク people are diverse. There are beginner-level オタク people, Kami(神)-level オタク people, and between-level オタク people. Some オタク don't accept beginner-level オタク as genuine オタク. It's complicating because many people have their own opinions about the border. So, saying アニメ好き might be useful in avoiding a conflict with a オタク or non-オタク person who has a strong belief about the border and the meaning of the word.
Please note that アニメ好き, マンガ好き and other 〜好き are essentially good words, however, it's possible that people having a prejudice use these words in a derogatory manner as explained by narutoさん.
My answer is a closer look at 「〜[好]{ず}き」, because I think this compound word is acceptable for most Japanese people, commonly used in everyday conversation, and proper in various situations.