Sarah, thank you for this great blog.
I think, the third point you made, suggesting introducing new people to others at church can be incredibly valuable.
Perhaps an extroverted personality will feel confident to meet people independently, but from my experience, as an introvert, I really appreciate the effort a person makes when they introduce me to others around and especially to include me in a conversation.
Part of the difficulty in a large church is that cliques seem to form so easily . Not wanting to blame the clique members, but, perhaps they become unaware that others, who are not in the cliques, may feel unwelcome to attempt to join in. Giving introductions and inclusive conversation would be polite and loving.
Perhaps the people who know how hard it is when we feel left out could use that experience to go out of their comfort zones and include others in conversations where they see a need.
Motivation for me comes from the pain of exclusion I have felt in the past, and not wanting others to feel left out and especially from the words of Jesus, " love your neighbour as yourself" (Matt 22:34:40).
Praying for God's help and wisdom is, perhaps, both a responsibility and a motivation. Reading your blog and writing this reply has alerted me to the fact that I have too often neglected my responsibility to pray regularly for opportunities to welcome and show interest in people at church.
Praise the Lord that He will use us as individuals even if our church doesn't have a 'greeting' system.
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