Then you should tell your priest to either deregister as a 501(c)(3) non-profit organization or to register as a 501(c)(4) & pay some taxes. It really is that simple.
It's what every single other non-profit organization that wants to involve themselves in the political process has done --- and it doesn't require passing any new laws.
However, if the bill was amended to include all 501(c)(3) orgs, it would mean that the ACLU, People for the American Way, Planned Parenthood, etc could all lobby, endorse, etc without paying any taxes. That would be the consequence of extending the bill to everyone.
As it is now, non-profit churches are treated exactly the same way as everyone else under these laws -- isn't that what people always say they want? -- for churches to be treated the same as everyone else?