Even if some people don't want to admit it , everyone should understand that both exchanges and debit cards services defeat the whole purpose of using Bitcoin in the first place because they ask you to send your real information's while you are probably using Bitcoin because it's anonymous .
So , It really depends on you and you only (and how much you care about your privacy) . I personally wouldn't send them anything .
I will also prefer to not send them anything, but if you need badly that debit card, I can send them my ID. Of course this way they will have only 1 of my btc address, while I can remain anonymous with for example the other 99 addresses I use, so not a very big problem for me in the end.