Somehow I don't think abolishment of the Johnson Amendment would result in less religious involvement in politics.
It's a very large interconnected system.
The main effect of eliminating the tax free status for religious institutions would be a push toward charity involvement where instead of the charity work being part of the church, the church would be a part of the charity (think basement soup kitchens and the like). Instead of having "St Mary's church and Soup Kitchen" you'd have a big legal shuffle that accomplishes nothing resulting in org titles like "St Mary's Soup Kitchen and Related Worship Services"
Unless they're proposing complete elimination of all tax-exempt status for all orgs including charities and similar orgs. Which would be interesting to think about but probably impractical?