At the time Jefferson wrote that letter, there was a "federalist party" and a "republican party" -- all lowercase -- because these were the names of the factions in the Cabinet and Congress. Had Hamilton or Jefferson attempted to form an actual political party in the British mold, Washington would have been forced to stifle his impulse to go to the stables, procure the stoutest horsewhip and apply it liberally to the backsides of both men. Washington was deadly serious when he spoke of "the baneful effects of political parties."
The letter captures a time when the factions still behaved with some sense of decorum. That would end with Washington's funeral.