I don’t think the author was referring at all to the threat of revoking tax exempt status of churches that engage in politics. That is a whole different issue than the one the author draws attention to.
But threatening a church with denying their tax exemption is something that I am sure Fred Thompson is against because it is antithetical to the philosophy of Federalism which he espouses.
The problem with ‘churches’ and their tax exemptions arose with the so-called ‘Church of Scientology’. This cult was notorious for their tax evasion antics and for blurring the definition of what was considered a ‘church’. In my view they are con artists. The reaction on the part of federal government to threaten any church’s tax exempt status if they were in any way engaging in politics, was deplorable. It punished all legitimate churches for the egregious behavior of a fraudulent cult, Scientology.
The problem here is not churches or in the definition of churches but with the Income tax. The solution is the FairTax, HR 25 (http://www.fairtax.org). And one of Fred Thompson’s closest friends and advisors is a strong supporter and cosponsor of HR 25.