CalledOutOne,
The history of the altar goes a little something like this. In the earliest years of the church, when celebrating the Lord's Supper, they tried to imitate the sequence of events on the night on which Jesus was betrayed. That included the use of a table when celebrating the Supper. The communicants would actually literally come to the table and stand or sit around it as they received the Elements.
It's not known exactly why the shift was made to having the communicants receive the Elements away from the table, but it is known that starting in the 6th century churches began restricting laypersons from approaching the table, and that is where the rails were introduced that are still often included in many churches: to keep people out of the table "zone."
Incidentally, for reasons I'm not entirely clear on, they called their tables "altars." This would later become a sticking point during the Reformation, because the Roman Catholics could point back to antiquity and say, "See? Proof that the Holy Church has always regarded it as an unbloody sacrifice! It's an altar!" Thus, many Protestants, in reforming the practice, insisted on calling it the Lord's Table, as per the first letter to the Corinthians. Naturally, though, less reformed churches, such as the Church of England, the Methodists, and the Lutherans, had fewer scruples about calling it an altar, and they continue to do so to this day.
But within Reformed circles, here is what I imagine has taken place. (This part of the history I don't know; I only speculate.) You Reformed Baptists started out as Puritans, and the Puritans started out in the Church of England. When the Puritans tried to find unity with the Church of Scotland during the English Civil War, there was a big row at the Westminster Assembly over the Scottish practice of celebrating the Supper at a single table, dividing the church into installments to accommodate numbers. The Puritans, much like the Baptists of today, were congregationalist. They were mortally offended that anyone would suggest splitting up the congregation, because they believed the proper "seat" of the ordinance wasn't in just any group of Christians gathered together but in an entire congregation. So they retained the practice of putting the table up front for show, but had the minister walk up and down the aisle with the bread and cup to distribute them. What I'm guessing happened, is both the tradition of calling it an altar and of taking communion in the pews got passed down to the early Reformed Baptists and was just reinforced later on as they started to sing Anglican and Methodist hymns and interact with Anglican and Methodist theology during the revivals of the Great Awakenings.