I have heard and read more than once (but can not find the haddith or ruling on short notice) that you should not cut your hair so that it is long in the front and shorter in the back, whatever that means. I think they say it is deceiving. I am not really sure about it. Kind of reminds me of those bob haircuts you see sometimes.
Anyway, it is not your intention to look like a non-believer, and I don't really think there is any particular "non-believer" style. Except maybe, some Buddhists monks and nuns shave their head, hasidic Jews have those long curly sideburns, stuff like that. But not all Buddhists or Jews have that same hair style, you know? You are not intentionally looking at a recognizably religious style hair cut and saying, hey, I want to do my hair like that. Just don't cut it like a boy's hair cut.
I know some churches don't allow women to cut their hair, but lots of women everywhere have long hair, whether it is for traditional reasons, religious reasons, or just personal choice. (It always seems that religion and hair are connected somehow.)
I recently cut my hair short after 13 years. I really regret it now. I wasn't growing it so long for any religious reason, just wanted to see how long it would get.