Yes, I've had this happen, and it has usually been Christians. My experience of other religions has been limited, but I've known Jews, Hindus, one Parsee (happy to explain when asked, and her explanation was fascinating), many Pagans of various traditions and quite a few Buddhists, and with the exception of one particular group of Buddhists, none have ever tried to convert me.
The Buddhist thing was interesting, though, in terms of what it taught me about the whole 'conversion' impulse. I was. for a short while in my teens, a member of Nichiren Shoshu, one of the few branches of Buddhism that actively prosyletizes. Like many a new convert, I tried my best at this and ended up annoying a whole lot of people - but ironically, they were often people who'd spent much of the last few years trying to convert me to Christianity!
Having been there, I will say this. One, when you're new to a religion you're in a honeymoon period, you haven't yet had the soul-searching or struggling that may beset people when they encounter difficult questions or life crises, and of course you will want to turn on as many people as possible to this wonderful thing that has changed your life, so you think. (To add to the complication, I was at the time madly in love with the guy who prosyletized me. I rapidly fell out of love with the religion when it became clear that he wasn't interested in me. This is superficial, but I'm sure it must happen, especially among young converts.)
Two, I think there's always a degree of insecurity, however subconscious, among anyone taking up something that the majority of people don't believe. Getting other people to share your belief makes you feel more secure, so you have an urge to convert others. It's easy to disguise this by saying you want other people to be 'saved', but trust me, that urge is there underneath. If you're simply trying to save souls, the appropriate response to those who won't listen is pity. Instead, what most prosyletizers show to the 'unsaved' is scorn and sometimes downright hatred. It only makes sense if it's based on fear of people who don't believe the same thing.
I used to get into arguments with street preacher types, but nowadays I just ignore them. Door-to-door people are interesting. Jehovah's Witnesses, we've found, will usually scarper at the mention of Paganism, but Latter Day Saints may come in for a cup of something non-caffeinated and a friendly chat.
_________________
"Grunge? Isn't that some gross shade of greenish orange?"