My sincere apology to anyone who was offended by the original version of this post. I wasn't trying to make unfair blanket statements about the diversity or lack of diversity in churches, and I certainly wasn't saying that Jesus is not present in Protestant churches, although unfortunately those were logical conclusions from my writing. I was trying to talk about what I've seen during my (short) experience going to Mass, and to emphasize that the Church offers a physical place to be with Jesus. Hopefully this revision more accurately reflects that.
One of the things I love about Mass is that there are usually people who look like they don't belong. The homeless come to Mass. The mentally ill and retarded. The questionably dressed. The very rich, the very poor. People of many cultures. People with a lot of faith, people with just a little; any (American) Catholic church on Easter or Christmas will be packed with people who only go to Mass a few times a year. I used to think this was a reason to condemn the Catholic faith - too many cultural Catholics, just going through the motions. But- shouldn't the church be packed with 'sinners'? Or is there another place they should be?
I can't pretend to know exactly why the Catholic Church is diverse. On an academic level, it probably has something to do with the timelessness of liturgy, that the Church is in every country, and the fact that no one can start a 'splinter' Catholic church. But on a spiritual level, it probably has to do with the fact that Jesus is present every day, all day, right there on the altar in the appearance of a bland communion wafer, as most churches continually display a blessed host for people to come and pray before. Every person who consumes the Eucharist (host, wine) experiences physical union with Christ, and even to spend time in front of the Eucharist is to be in his presence, guaranteed. So maybe the answer is just, of course the Church attracts all people - Jesus attracts all people.