This situation is very common. If your priest is not fresh out of Seminary, he has dealt with similar situations in the past.
I was one such. People at one of the parishes I was visiting thought I was Catholic, and there were circumstances that made me feel that it was best not to enlighten them. I wasn’t hiding, but at the same time, I had become involved with a group of friends there, and it seemed best to me to leave them under the impression that I was Catholic. (I never received Holy Communion there, but no one ever noticed that.) Over the course of time we became involved in various activities that, while not absolutely forbidden to non-Catholics, would have caused eye-brows to rise.
When I made the move to actually become Catholic, they became aware of my RCIA journey - and they were my staunchest supporters. Far from turning away shocked or disappointed, they walked with me the whole way, bought me good books, furnished my home Altar, and taught me to say my prayers. Indeed, they supplied me with a kind of Catholic childhood and parented me into the Church in a way that no RCIA is capable of doing - they were my
true godparents.
I used to think I was the only one, and then I became aware of a great many others. The stranger you sit near at Mass may well be a non-Catholic visitor who is wondering how to “out” himself or herself.