By adding a tax, you are narrowing that separation. The original bargain was the state wouldn't recognize an official religion and religions would be tax exempt - a good enough attempt at keeping the institutions separate.
This is problematic on its own, but becomes worse if the tax laws don't result in equal treatment. For instance, a rule that exempted collections on Sunday from taxes, but not any other day results in favoring some religions, even if the rule is applied equally to all.
And the extreme case is that the government could just tax all religious orgs out of business, leaving us with religious freedom, but not any churches to join.
No, it wasn't. Tax exemption of churches isn’t the result of a “bargain” between exempt churches and the state, and isn’t a premise for state neutrality toward religion (either in the US or, as is actually relevant to the article but surprisingly not what most comments focus on, Canada.)