Does Riot still allow skin trades?

You are and have always been allowed to buy a skin for a friend. Your friend is also allowed to buy a skin for you. Whatever arrangement you make with said friend is not of any concern to Riot.

But - And I want to stress I am not singling out OP with this additional comment, but rather mean it as a general address :

You are a MORON if you accept a 'skin trade' with some random stranger on your friend list.

i think he means

"i have this skin that you want, you have that skin i want, lets trade"

and the answer is no, that's not a feature (unfortunately).