If it were me, I think I would try to phrase my welcoming intentions more positively. So instead of explicitly saying something like "we might let in people you don't agree with, so be prepared to deal" () I would try to develop (with the input of your current families) a list of values and expectations that represent your group and its goals that could serve as a unifying thing, even if families come from different faith backgrounds or social situations. These could be educational and interpersonal values, things like "fostering intellectual curiosity" "encouraging independence and critical thinking" "practicing respect for adults and fellow students" "expanding horizons by learning about cultural differences and relating to people from diverse backgrounds" "modeling thoughtful dialogue and tolerance for differing views" "commitment to regular attendance and sharing in preparation and planning responsibilities" "learning to work productively in groups" Whatever fits your group. Then any family that could affirm those values/goals would theoretically be welcome. You could make them more explicitly Christian, if that fit too.
I think if your aim is to have a diverse group, it might be wise to have some understanding about topics that would not be "taught" at the group. It might be best to keep theology and politics instruction in the homes and focus on areas where there is most likely lots of agreement. It is easier to not start something in the first place than it is to stop something because some people find it objectionable.
Also, it might be good to decide if you are a Christian group (albeit one that is open to Christians of any stripe) or are you a homeschool group that is made of a Christians at the moment (but non-Christians would be welcome in the future). Do you want people to at least affirm some very basic Christian faith statement (like maybe the Apostle's creed) or would no Christian commitment be expected? If non-Christians are welcome, would they be expected to tolerate a certain level of Christian practice at meetings (will you open in prayer, make use of church buildings, use some Christian materials, celebrate Christian holidays)? How much sharing about a parent's personal worldview beliefs would be considered appropriate in the co-op setting if they are not views shared by others in the group?
I think a membership policy is a good idea. If I were joining a group I would expect to see things about:
how parents would be expected to share in the planning of meetings or instruction (assuming you aren't hiring tutors)
how money issues are to be handled (Is there a fee per meeting or per month or semester to cover snacks, craft supplies, copies, and other materials? Is there a way for parents to get reimbursed for what they spend preparing a session or is it more like a donation and everyone takes turns doing their part? If there are field trips or such things that require paid reservations, who collects the money/puts things on their credit card? Do you have a bank account for the co-op? Who keeps the books? Are there refunds? You might want to elect a treasurer or something.)
basic expectations for how children are to behave and relate to one another and other parents
a simple admin procedure for how conflicts or disciplinary issues will be handled (i.e. who do complaints go to and who is in charge of making decisions about how they are resolved. Might be good to have an elected person in charge of this kind of thing)
details about when the group is open to new members and how one joins (always open, only at the beginning of a school year, by semester, do you have to have a referral from a current member family, can you attend for a certain number of weeks to try it out before committing)
If you are starting out small, you probably don't have to have everything figured out on the outset and what you need to clarify will become more obvious as you move forward. There are always going to be things you couldn't have foreseen or planned for with this type of thing.
How exciting! I hope it turns out to be more blessings than headaches as you get stuff off the ground.