From your perspective it is an annoyance.
On the contrary, I find it interesting to talk with people about religion. I welcome neighbors, strangers, homeless people, and door to door people to talk with me.
What I find annoying and why I say I have only encountered people trying to add to their group, not actually spread love and faith, is because none of them could take "no" for an answer. Tellingly, none could take "no" for an answer even though they claimed to be Christian and I go to a Christian church already. Somehow, that just wasn't good enough.
That indicates to me that it wasn't about sharing Christ's message or about loving me. It was about them being threatened by any person who was strongly standing in her faith, but whose beliefs and congregational affiliation was not the same as their own.
I can contrast this with numerous friends and acquaintances who, after meeting them early in our relationship, invited me to church or shared their faith with me. I shared mine with them and told them I had a church, and they were excited and happy for me.
I am sure there are some churches who truly are about going out and loving others and spreading faith. I just haven't met them at my door yet. So far in my experience, the more prone to door-knocking a denomination/church is, the more intolerant they are of other churches and Christians, let alone people of other faiths.
To come to my door is not the annoyance. To not take no for an answer is.
Those of you who are annoyed by door knockers don't need a physician, but wouldn't you be so kind as to put up an occasional annoyance for the sake of those who do. Someone who comes to your door won't know you are not sick until you answer. In which case, they will move on to the highways and by-ways until they do find one in need.
I put up with it, and I am kind about it, despite being annoyed at people's tendency to think my beliefs are irrelevant or errant and that their own are superior, and despite their insistence that their little group is the only way to Christ. I think it's just human nature to think this way, so I will continue to discuss with them until they are tired of me. I'm warm and friendly. I still think it's an invasion of my privacy and that the general attitude is arrogance, but that doesn't mean I am mean to them. I figure everyone needs kindness and to be heard.
It's not my own way of spreading the Gospel- I wait until I feel called to talk to a particular person, and that small still voice within tends to lead me to those who need me to be with them spiritually. But I tolerate that other people do this. Upon probing, I find most seem to do it out of fear for others rather than out of love and joy, but it's still based (even though I think in a problematic way) on concern for others. I can appreciate the concern, though I don't appreciate the delivery.