Wow ... this is a really good question. I must admit, I never thought about this. There are like dozens of "legit" etherium tokens, and 100s of crap-tokens, which would all be copied. Could coins like "Osmise GO Classic" and "Civic Classic" be a thing? Man ... what a mess that could be ....
The forked just give an impact to the main token just like ethereum and all of the asset will be the same and there will be no change in the ico just like eth and etc. So don't worry about that your asset will be fine.