First, churches are not at all prevented from speaking aout on any moral or politcal issue of the day. Those who claim they are are either woefully misguided or lying.
However, if they are registered as a 501(c)(3), i.e. non-profit, church then they are forbidden from endorsing candidates, most political lobbying, etc. This is the same exact rule/law for every single 501(c)(3) organization in the U.S. from the ACLU to the NRA.
It's not required anywhere in U.S. law that a church register as a non-profit organization. If a church does want to endorse a candidate, lobby, etc they can either deregister themselves or form a 501(c)(4) -- which is exactly what the ACLU, NRA and thousands of other organizations have done.
Instead, supporters of this bill want to carve out a special exemption for themselves -- and not other non-profit organizations -- so that they won't have to pay taxes but can still engage in political activity when, again, the real answer is to deregister or register with the IRS in a slightly different manner.