According to the oldest understanding of Jewish law, a person is a Jew either through having being born to a Jewish mother, or through undergoing a rigorous, intense conversion. (Please Note - conversion in general is a hotbed for all kinds of issues which cross the borderline of politics. I generally try to avoid dealing with it as I am not an expert in the laws of conversion.)
Every mohel, when asked to perform a bris, will ascertain that the mother of the baby is Jewish either by birth or through an acceptable conversion process (unfortunately, some conversion programs are not very serious in their instruction or demands on observance of the Torah's laws). This would automatically make the baby born to her Jewish, and fit to have a bris in its proper time.
The mohel will not ask about personal observance or religiosity, because it is irrelevant to his job (unless he is thinking of grabbing a bagel or danish to go, in which case he may want to know if the food is kosher.)
When the mother or baby is a convert, or planning conversion, some mohels deal with this regularly, while some shy away from it unless they work with the first hand guidance of a rabbi who will help them through the steps of the conversion process.
The main thing to do is have an open conversation with the mohel. Recognize where he is coming from, where you are coming from, and understand that the mohel knows as well as you know, that this is a sensitive issue.
And if the mohel can't take the job for personal reasons, don't take it personally. He has personal and religious standards regarding whose Jewish status is unquestioned in Halakha (Jewish law), and therefore which babies he can circumcise in a bris ceremony.
He typically does not mean to offend you. You just might need a different kind of mohel who is not Orthodox.
