An amusing anecdote from the Old Oligarch reminds me of two others in a more or less similar vein.
Firstly, I was once accosted by a Protestant 'sidewalk evangelist' who was asking people 'Would you like to come to a non-denominational church service?' At a loss for time to engage with him more thoroughly, I replied 'No thanks, I'm a very demoniational sort of person.'
Secondly, the late Father Bouyer, in his excellent biography of Newman (about which, more anon) recounts the incident of a newly appointed Anglican clergyman calling on the aged Cardinal at the Birmingham Oratory so that he might pay a pastoral visit on his 'most distinguished parishioner'. This mirrors an event several decades previously, when as an enthusiastic new pastor of the Anglican parish of St. Mary the Virgin, Newman himself began an intensive programme of visitation. He called in on regular churchgoers, lapsed churchgoers, dissenters and on one particular gentleman who was known not to attend either the established or dissenting services. He turned out, to Newman's surprise, be a Jesuit who was tending to the spiritual needs of the Catholics of the area.