Most Episcopal churches have red front doors, and, as a boy growing up in Washington, I noticed that the red door was pretty common for other denominations. I've seen it on Lutheran, Methodist, and other churches. As usual with traditions, there are a lot of suggested reasons for the red door. One website collected several; here's the one I like best:
The red door tradition originated during the Middle Ages in England when it was a sign of sanctuary. In those days, if one who was being pursued by the local populace, shire reeve (sheriff) or gentry could reach the church door he/she would be safe. Nobody would dare to do violence on hallowed ground and, in any case, the Church was not subject to civil law. The red door was fair warning to pursuers that they could proceed no further. One who claimed sanctuary in this way would then be able to present his/her case before the priest and ask that justice be served.
These days, many who claim the name of "Christian" actually demean or even attack people who are unlike themselves. It is not so with us.
In my few years with the Episcopal Church, I've met quite a variety of people: rich, poor, black, white, college professors, mentally handicapped, gay, straight, transgender, We've got judges and ex-convicts. It's remarkable that all these people get along; it's extremely remarkable that there's nothing remarkable about it. Being gay is the biggest non-issue in the place. Nobody sees any point in talking about it.
We need to remember that red door. People who are called "unworthy" by American culture really are welcome here and we will do what we can to help you feel at home.