You will probably not make friends by merely shaking hands with strangers.
First, you have to recognize that they are not “strangers,” they are your brothers and sisters in Christ, members of your Church family.
Second, you have to get beyond just “meeting and greeting” and shaking hands. You have to talk. Converse. Discuss. Try asking questions of those you are shaking hands with. Get to know them a little.
Third, select people who will be realistic possibilities as future friends. Certainly we should be friendly and greet anyone that God brings into our sphere. But if you are looking for friends, seek out people who are close to your own age, and who appear to be in the same life situation that you are in. E.g., if you are young parents, put more time into greeting other young parents. Or if you are retired, put more time into greeting other retirees. Yes, you might be able to find a close friend among people who are totally different than you, but logically, you’re more likely to become close friends with someone who shares your age, life situation, income level, time availability, sex, etc.
Fourth, eventually, get beyond just “meeting and greeting” and talking, and ASK your potential friends to go our for breakfast, lunch, dinner, coffee, a drink, etc. It’s kind of difficult to be “friends” when the only time you see each other is before or after Mass. You have to do things together, and often, eating/drinking together is a great way to get started. I personally would invite someone to a restaurant or coffee shop at first, but only because I’m a little wary of asking someone that I don’t really know well to come to my house. But perhaps you’re more open than I am. At any rate, ASK. If they say "no,’ don’t take it personally; people often have already made their plans. But I can tell you that if you asked ME out to coffee after a Mass, I would probably go with joy! I love making new friends in the Body of Christ!
Finally–and I say this with kindness–try to lose the “attitude.” If you walk around with the attitude that “this is a pointless gesture,” you’ll never make friends during a “meet and greet” time. If you have other ways of making friends among those who attend your parish, then perhaps for you it is a pointless gesture and don’t worry about it. But the best attitude would be to look at “meet and greet” times as opportunities to make contacts with fellow Christians who are all trying to follow Jesus and make it to heaven, not as some kind of “intrusion” into your Mass time.
I hope this post is helpful to you and others. Good luck to you!

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