I will allow that there are going to be some innocent mixups. But the 'democrat party' epithet dates back almost a century. https://en.wikipedia.org/wiki/Democrat_Party_(epithet)

If you care about the perception of what you write, this is one of those things that will quickly steer your audience one way or the other. It has become so consistent that I would personally try not to get it wrong lest it distract from the point I'm trying to express.

I didn't write "Democrat Party", I wrote "Democrat-Dominated". I am a registered Democrat. The broader partisan group I belong to are "Democrats" even if the organization formally calls itself the "Democratic party".