If they're close enough friends that you want them there and there's enough room in the chapel invite them. We have . dd1 is making hers next Saturday and our best friend who is an atheist is coming to both the chapel and the do afterwards.
I'd invite them but make it clear they are welcome to come along to the coffee etc whether or not they choose to come to the church - people vary in whether they'll sit through a religious service or would feel uncomfortable/hypocritical about it, and some people would feel awkward about coming to the "party" if you don't make it clear you'd be happy about that.
Why not as long as your local Parish and Minister are happy what is the issue, just make it clear that you understand if they don't wish to.
We've been invited to our best friend's child's ones. We're both practicing pagans and my husband was the elder child's godparent despite them being RC. Their church are very open, friendly and welcoming to other religions/aetheists.