tub: "open wooden vessel," c.1386, from M.L.G., M.Du., or M.Flem. tubbe, of uncertain origin. Related to O.H.G. zubar "vessel with two handles, wine vessel," Ger. Zuber. Considered to be unrelated to L. tubus (see tube); one theory connects it to the root of two based on the number of handles. Also 17c. slang for "pulpit;" hence tub-thumper (1662) "speaker or preacher who thumps the pulpit for emphasis."
Which is why in BE, tub-thumper is a common way of referring to politicians (as is my understanding), especially populist demagogues or reactionaries blinded by ideology.The origins of this phrase can be found at the end of bibliolept's post. A tub-thumper is a speaker or preacher who for emphasis thumps the pulpit; a ranter.
Typically, a tub-thumper has extreme views of some kind and is never going to change those views. His (they are almost always male) aim in life is to convince the world to accept his views, and to completely ignore any suggestion that he is wrong. Imagine someone speaking in public with that degree of self-confidence and self-deluded authority.