(1) Look at Tom Jeff's actions. He preached a nominal Christian faith, in an official capacity. The encroachment he disagreed with was that of one flavor of Christianity upon another; to him it was beyond question that a general Christianity should continue to be preached. (2) The letter was a promise not to interfere in the Baptists' exercise of faith, not a barrier to forbid Baptists to exercise a general Christian influence in official affairs. (3) Thomas Jefferson was not exactly an expert on the context of the First Amendment in the first place; he was off in France when it was codified.
In other words you do not have a smoking gun here. Modern eyes construe the excerpt, especially out of context, quite differently from the way that Thomas Jefferson himself did.
I fail to see how removing the two words added in 1954 threatens our Republic.