The meta is just what players deem to be the most effective way to play the game, so think of it as a standard. If you want to do something different, you're perfectly able to do so. People might be annoyed (especially in ranked), but it's not against the rules as long as you're still trying to win the game.
Especially if you're playing normals, just play to have fun and don't worry too much about what other people think. If you want to climb the ranked ladder, you don't have to play "meta" picks, but you might want to avoid really strange stuff (like AP Ashe or something) if you want to have a good chance of winning.
It depends. I think if you stick to normals and tell people before hand you're trying something off-meta, then people shouldn't have a problem. However, if you go full AP Zed, people are obviously going to be annoyed. On the other hand, if you're trying something because you genuinely think it can work, more power to you. (Maokai support OP)
It is looked down upon because, as PsiGuard said, the meta is deemed to be "the most effective way to play the game", and some people just care about winning too much.
In some cases it's just people being too picky on rankeds (i.e. getting mad because you didn't pick the current strongest pick for your lane) or tryharding on normals. If you go with too weird/useless stuff in a ranked game you're just going too far though. Try AP Garen in normals only please.
Then there's those offmeta picks/builds that end up being meta after the average player realises it's a strong pick/build (e.g. tank Akali back when it worked, the first instances of Annie support, etc.). In those cases you can only educate them by showing how strong this new pick is ;P
Especially if you're playing normals, just play to have fun and don't worry too much about what other people think. If you want to climb the ranked ladder, you don't have to play "meta" picks, but you might want to avoid really strange stuff (like AP Ashe or something) if you want to have a good chance of winning.
In some cases it's just people being too picky on rankeds (i.e. getting mad because you didn't pick the current strongest pick for your lane) or tryharding on normals. If you go with too weird/useless stuff in a ranked game you're just going too far though. Try AP
Then there's those offmeta picks/builds that end up being meta after the average player realises it's a strong pick/build (e.g. tank