This story is most likely untrue according to snopes The phot is actually of a homeless man in London. A Tennessee pastor did go undercover as a homeless man it his year.He did find church people who offered aid. He also found help on the streets from passersby and other homeless people.

Things might be more complex than this story implies. This congregation might have a huge outreach program for the poor. There might be free meals every day, food banks, etc. Churches serve many functions, service to the poor is just one, perhaps the most important but still just one. If there were other programs to serve the poor begging at church services might be legitimately discouraged.

I spent 8 months in Mexico and one thing my Mexican friends told me was never give any money to people begging when you're eating in an outdoor restaurant. I came to see the wisdom in that advice and had to harden my heart. So I can see a possible justification for the member's behavior at the church service.

Added: As I pondered this post I remembered. Some years ago I used to take my dog to the church of St. Francis for free health care. They also ran a lunch and dinner program for the poor. During the times they offered these free services out the back entrance the other portions of the church were closed.