You know who else gets tax exemptions? Universities. The largest landowner in the city of Philadelphia is UPenn. They pay no property taxes whatsoever.
People calling for churches to be taxed maybe don't realize this, but churches don't make money these days. Hospitals and universities in cities occupy large tracts of extremely valuable land, bring in tons of revenue, and pay no taxes.
I'm fine if you want to do away with tax exemptions, but at least apply it fairly. Targeting a specific type of tax exempt entity, the one with by far the least ability to pay in most cases, isn't a sincerely thought out policy stance. It's simply open hostility to the existence of churches, usually with absolutely zero regard for either what those churches do, or whether they could even afford to pay the tax bill.
Some of those churches - and I'll give you one guess as to which city population would have the most closures - would probably not be able to stay open. Many churches can barely afford to keep the lights on and pay staff, and some can't really even afford those things. Taking people's churches away hurts them. It's not progressive or good to hurt people to make a stupid point about religion.
Churches aren't the only ones I'd remove tax breaks from. Anything that masquerades as a charity but isn't. In the UK that would be public (which are actually private) schools and "educational" bodies that exist to push a political viewpoint like the Institute for Economic Affairs. Wouldn't be hospitals or universities here. You say churches would be hard up, let their members support them, not the general public through tax breaks.