Yup, I am surprised and not suprised at the same time. They want your parish "membership" but I am shocked they wouldn't be more worried about your child's mortal soul.
My husband and I are Catholic - I went to Catholic school for 13 years - and we have baptized our children Catholic. We plan to have them recieve their First Eucharist in the Catholic Church and are doing religious ed as part of this. We are not rigorous church attenders. We plan to go more now that our daughter is going to make her first communion. After that, we plan to attend the Unitarian Meetings near us and have our kids do Sunday school there, unless they express a preference to attend the Catholic mass.
I do feel the part of a hypocrit here, but my husband and I are so NOT in sync with the Church for a variety of reasons. I feel like we owe it to our daughters to share their heritage with them and give them the background and experiences to practice Catholocism. At the same time, there are many things we just can't identify with or justify, and I feel the need to share that with them too.
So, the sort answer to your post is to look at Unitarian congregarions. All my research suggests they focus more on spirituality and religion as different ways of addressing faith and take a global world appreciation of religion rather than adhereing to any one dogma. Lots of "mixed" religion couples do this.
I also have a friend who attends an Episcopal Church. They are very simlar to Catholic, and that might work for you to feel comfortable in a more traditional but open church setting.
All Catholic Churches are not created equal either - our very conservative diosese is very difficult to take. But we attend a more open and friendly Selesian-run church (non-diosocean) and I grew up with Jesulits and Sisters of Mercy who were wonderful.
Added: My SIL had her child baptized in her mother's church, since she doesn't really attend church, so that's another idea - go to a parent's parish.
By no means do I mean to discourage you from practicing your faith, and I also understand the church's desire to have parishoners take priority over people who don't attend (they do the envelope thing for prioritizing students for a Catholic school near us too.) Just sharing some options :)