This may be related to their government wanting all businesses to record who their customers are:
“Why are you requiring certain businesses to record information about customers?
One of the primary means for transmission of COVID-19 is in-person interactions that last more than a few minutes. By recording customer names, businesses will enable the Kansas City Health Department to more quickly trace, test, and isolate individuals who may have been exposed to COVID-19 if an employee or customer had the virus at the time they frequented the business. All data obtained by the Department of Public Health will remain confidential and will be used only to address public health concerns and contact individuals who may have been exposed to COVID-19.”
I read more on the website, and it says if a patron sits at a business for 10 minutes, like in a beauty salon. That may be why this would include churches. Still, who wants that?
From your link:
“Are religious services, wedding, and funerals allowed?
Yes, after May 6, in-person religious gatherings (including weddings and funerals) may resume, subject to the 10/10/10 rule (if held inside) or limited to 50 people outside, provided social distancing precautions are followed and event organizers maintain records of all attendees.”