I think that coffee and donuts, either in Protestant or Catholic churches, or in a secular setting (e.g. a community club) is a very poor way to meet people, as the “social types” flit about and network, while all the shy types sit about and say nothing unless they are spoken to. Also, it’s unhealthy.
**My suggestion to the OP **is to select an activity or study in the parish that interests him, and attend. There, he will meet others of like-mindset in a small-group setting where it is easier to converse.
E.g., if he enjoys theater, he could join the group that attends theater productions. Or if he likes to garden, join the group that beautifies the church grounds. Or if he enjoys Bible study, join one of the Bible studies. etc.
I realize that not all parishes have a lush list of social opportunities. Well, then find a parish that does. In this day and age, it seems that the geographical boundaries aren’t as binding as they once were, and rather than languishing in a cold parish, it might be better to pull up stakes and move.
OR–another approach would be for the OP to work on stepping outside of his comfort zone and approaching some of the supposedly unfriendly people in his home parish and chatting with them. I’m guessing he would discover that many of these people are actually very friendly and warm-hearted, and he would make friends. The old saying is, “In order to make friends, you first have to BE a friend.” All too often, we expect everyone else to make the first move and then we complain when they don’t. Well, maybe the OP should make the first move and be a friend to those who appear to be closed and cold.
I realize that this is terrifying for someone who is shy. Perhaps some counselling (short term and therefore inexpensive) would help the OP to learn some social skills that would help him to overcome his shy practicies. Yes, he will probably always feel shy, but he doesn’t have to ACT shy. Try some counselling.
One more thing, to all the people on this thread. Mass is the time when we encounter Jesus, Truly Present. Yes, it’s pleasant when we are sitting with our big family or with a group of friends. But many people in the Scriptures encountered Jesus when they were all alone (e.g., St. Paul). The Lord Jesus should eclipse all else and attract our undivided attention at Mass. When He is present, all else fades.