well, I sent an e-mail to the Instagram support because I can't download Instagram using Google Play (in CM 7.1).
They answered this:
Hi Cristian, unfortunately we don't provide support for custom ROMs. This is probably why you are running into trouble. Sorry!
The Instagram Team
Anyway, I downloaded the apk and everything works fine, so I don't know why they don't support CM or MIUI at least
Phone: Galaxy Mini 2 (GT-S6500) White