The reason they want emails is because the phone calls are slowing the call center SLA to a crawl and tanking their metrics for the quarter. If this keeps up, the payment processor will push back next time and Christian authoritarians won't be able to get away with shenanigans like this again.
They probably have their customer support laid out as phone, email, and maybe chat. Phone is the most expensive support channel because it's 1 person to 1 problem and it's impossible to scale, so they can't roll out a bot or ignore the metrics for long. Keep up the pressure!