In the UK the tax people - the Inland Revenue (IRS) - decides what is and what isn't a charity.
That is because the primary benefit of being a charity is tax breaks.
Tax not received from charities has to be collected from other sources. 'Charitable status' is shorthand for 'tax subsidy'.
Nobody is being muzzled by potential removal of charitable status - merely holding their feet to the fire of what their original purpose was - if that purpose diverges too far into politics then they are no longer a charity by definition, and should seek funding apart from the taxpayer.
I also think that promoting religion should not attract taxpayer subsidy in this day and age - let them do a sale and leaseback of their property empires if they are hurting for cash....though God always needs a little more, doesn't he?