There is no such thing as an "Anime Style" anyway. Maybe things have homogenized a bit in the modern day because of budgetary and/or trending issues, but "anime" in Japan at least just means "animated". Even with specific genres (comics for younger boys, for young men, for girls, for ladies, for adults, etc.), it's not all the same look, either.
Our beef with what I'll call the "Animesque" style is that the artist generally doesn't seem to have any grasp of basic composition or anatomy and don't seem to be willing to accept even constructive criticism. Don't be the kind of person who rests on their laurels, continue to seek improvement and experimentation REGARDLESS OF STYLE, and most of us won't have a problem with you.
Plus, the TF2 world runs on Manry Men Doing Manry Things, so seeing our favorite death-tag playing sociopaths as androgynous pretty boys more interested soap-opera style drama than killing each other is a little off-putting, to say the least. In my opinon, Team Fortress 2 would be an AWESOME anime...one like Dragon Ball Z, Fist of the North Star, Jojo's Bizarre Adventure, Hajime no Ippo...etc. If you want to do TF2 anime-style fanart, do THAT, since it's a relatively unoccupied niche.