Divisiveness and redistribution
This sort of thing is an integral part of my objection to the redistributionist Leviathan State, and I guess it might even fall under the Alinskyite advice to force the enemy to live up to his own book of rules. (We conservatives are the counter-culture now, after all.)
We're always been told that "divisiveness" is one of the worst political sins. Few epithets come more readily to the leftist tongue than "divisive." Some of them throw it into nearly every reference they make to their political opponents, the same way they ritually chant accusations of "extremism" or "greed."
But what could possibly be more divisive than an overbearing regime of income redistribution? It's a system that transforms citizens from competitors into enemies. You can only get what you are "entitled" to by taking it from others - who are, by definition, unfairly seeking to "steal" your rightful due. Instead of attracting the attention of competing providers, the dependent citizen seeks the attention of benevolent politicians... and hopes to evade the notice of tax collectors.
Free people have daily control over their lives. If they no longer wish to patronize with a business, work for employers, or join forces with certain partners, they are free to change their minds (within contractual limits, of course.) A single individual's needs are of relatively high importance to those who compete for his business. It's not perfect, to be sure - we've all got stories of being treated badly by vendors and employers. But it's vastly better than the level of influence we enjoy as dependents of a massive, distant government.
We only get rare opportunities, separated by years, to directly influence the government. And our hopes of doing so are very small, unless we join a political collective - a union, an interest group, etc. Then we can get the attention of the political class, especially if the masters of our collective can assure their political allies that our votes will be packaged and delivered neatly on Election Day. That means solidarity with our collective is paramount. Politicians are not afraid of loose alliances whose members are liable to stay home on Election Day if displeased. They fear well-disciplined political troops far more than irregular electoral militias.
In sum, our system is designed to encourage and promote precisely the sort of factionalism you (and George Washington) denounce. In fact, failure to join such a faction is irrational. You are not going to be left alone - the ruling class has only just begun to seize your assets, regulate your life, and control your industry. You must march in lockstep with many others to find a measure of security... and you should learn to view your political opponents as bitter enemies, just like liberals do. You'll notice they're not shy about challenging the very humanity of people they disagree with. Factional warfare is a contest of morale, just like all other warfare is.