Objectivism is a philosophy, not a movement. There is no reason for Objectivism to be a movement.
It's perfectly fine the way it is, with people knowing exactly what it is, and free to subscribe to the philosophy, in whole or in part, and free to choose whether to work together for some common goal, or not. If it ever becomes a single, "open" movement, that movement will end up with leaders, and the leaders will want to add their own ideas to the tenets of the movement, and, since Ayn Rand was a genius, them and their ideas will end up not living up to her intellect...and then that will be that, because no one will care about another self-contradicting Libertarian political movement that can be thoroughly demolished by anyone with half a brain.
That's what an "open Objectivist movement" is, btw. : Libertarianism. They took a few really good ideas (mostly Ayn Rand's, and a few Economists'), formed a movement and opened it up to whatever ideas anyone willing to participate could come up with. Now their movement has religious fanatics, pacifists, anarchists, anarcho-socialists, protectionists, isolationists, nationalists, wackos and weirdos and dingbats and dodos... everything except for intellectually consistent defenders of individual rights.