Are there any particular Jewish communities where the congregants remove their shoes before entering the Beit Kneset?
In the Paradesi Synagogue in Kochi, India, everyone is required to remove their shoes upon entering.
Source: My wife and her family's personal experiences and Wikipedia.
Many Karaite communities pray barefoot in deference to Exodus 3:5.
It was the standard practice of Rabbinic Synagogues of the Middle east to take off their shoes. But as the modern European culture became the norm in the Middle East, people started wearing nice leather shoes and keeping them on. This same development occurred with prostration. Originally practiced by both the Rabbinic and Karaite Jews of the Middle East, the practice was abandoned by the Rabbinates as the influence of European clothing and chairs spread into their Synagogues.
Source for Karaites: https://books.google.com/books?id=hGILHIgEl7cC&pg=PA139&lpg=PA139&dq=karaites+barefoot&source=bl&ots=IVPlYDG5J6&sig=dToqSbroNIVSApzy50PwkG7Mq5k&hl=en&sa=X&ved=0ahUKEwikxNmh4rHKAhVWz2MKHeSbDHYQ6AEIHjAA#v=onepage&q=karaites%20barefoot&f=false