Marina, I'm a baptised Christian too, I just decided when I was about 6 that I didn't believe in God, and I have never wavered from that. Actually, there have been times when I wished I did! I have seen the strength DH draws from his faith, but you can't force yourself to believe something.
I am happy for DS to be raised Catholic, but the agreement I have with DH is that if DS decides at a latter stage that he wants to be atheist/humanist/buddhist/jedi, then that must be respected by both of us. I'm not sure why, but I think it's easier to have a religious background and choose to give it up, rather than be raised without a religion and then choose to follow a faith later in life. But that is just my personal view. .
Anyway, re your question about godparents, I am perfectly happy for DS's godparents to send him anniversary cards, Christian storybooks etc. That's part of their role.
I am actually a godparent to several children (including a couple of Catholics) - I supposed the term shouldn't really be "god"parent. I don't send my godchildren bibles etc, but I do send them good books, they have religious godparents for their religious education, I have another role. Does that make sense?