The philosophy of Objectivism is separate from a movement based on the namesake. In addition Objectivism is also not the libertarian movement and is in fact quite different from it. This does not mean that one cannot be an Objectivist and support a Capital L Libertarian Party Candidate or even be a member of said party. (Although Diana Brickell from Philosophy In Action whom I greatly admire presents the counter case on her podcast.) One needs to distinct movements from people in order do understand why I say this. As well as movements from individual parties or party members.
I fully agree with Diana Brickell that Objectivism and the libertarian movement are not inherently allies. In fact, there is a fair portion of the broader libertarian movement that is filled with relativistic and subjectivistic types of people. It is also filled to the brim with Anarcho-Capitalists and anarchy supporting factions.
I also agree with Diana that anarchism is a majority in the broader libertarian movement and has been since the movement began. I, in addition agree that anarchism in any form leads to a world just as bad if not worse than the tyrannies of the various overbearing governments on the world stage. However, it is the libertarian movement that I feel Objectivists need to stay away from or any rational person. Not anything with the label Libertarian on it persay. There is a difference between a Capital L Libertarian Party member or supporter and agreeing with the broader small l libertarian movement as a whole.
I agree with Ayn Rand actually that the lower l libertarian movement is basically the hippies of the right. However, I also do not think this is the same as Capital L Libertarian support at all. One denotes supporting a specific political Party and its platforms. While the lower case l is to agree with the idea that all that matters is a Non-Aggression Axiom devoid of any foundation or reason to support it. It also may or may not consist of a view that acknowledges protection of rights due to this mistake in primary premises.
However, the various Libertarian Parties all over the world are all very different. Some do condone and even support the disaster that is anarchism. As well as supporting subjectivism and nihilism on top of that. While other Libertarian Parties are fully for limited government and go out of there way to provide evidence for their limited government stances. I know one leader of a Party that is specifically anti-anarchist in his platform as it calls for very moderate proposals. He also too like me is an Objectivist as well.
There are some Libertarian Parties and institutes people of reason and reality should not associate with or support. These would be any Parties endorsing unreason or even non-reason. Any Parties that fully support, endorse or fail to call out the anti-rights view of anarchism. These Parties one should not provide support and cover for. This would also be institutions of "liberty" that support or push anarchism as the ideal. Or any institutions which proclaim reality does not exist as a primary value or view.
However, one needs to take an individualistic stance when dealing with libertarians, Libertarians and Libertarian Parties. Some are part of the broader lower case intellectual movement and are supportive of very bad ideas and others are just fine. Also, one should never judge individual libertarians as less than good just because they are libertarians as you might be speaking to someone just as anti-anarchist and pro-reason as you are. It needs to be taken on a case by case basis in regards to this specific rule of thumb.
I want to also mention something else as well this time to do with The Objectivist Movement as well. Not everyone that claims to be an Objectivist is going to be fully using reason either. There are a sizable amount of people that become Objectivist in label, but, use it as an easy justification for being a dickhead or even abusive. Diana Bickell calls these people Predatory Egoists. People whom claim the mantel of Objectivist or Rational Egoism only to fully ignore the need for being ethical or rational. Essentially using the "movement" and involvement in it as a way of controlling others or becoming Pseudo-Authorities of Objecrtivism to laud over people.
Being an Objectivist is no indication on whether someone will be fully understanding of the need for virtues to gain values. Nor understand what the virtues mean nor understand that mistreatment is not being egoistic, but, instead is being a bully, dogmatists, insular and a horrible human being. Once again one needs to take an individualistic treatment and acknowledge Objectivism is not a collective of its own. Some people will be claiming to be so and not even understand the philosophy they claim to represent. Others will know the philosophy, but, misuse it. Some are just plain toxic people and would be toxic without the philosophy. If someone is already toxic becoming self loving even more would push them to be even more toxic. People can be evil with any label.
In short, Objectivism is not libertarianism and is not libertarian it is Objectivism. However, one can be supportive of the better Libertarians and love/admire and even associate with individual libertarians just like any other individual that is not an Objectivst. If Objectivists judged all other people as being worthy of benevolence and good will on the basis of sharing our same philosophy Objectivism would indeed be the very cult its detractors claim it is. If this were true I would flee from it as I do from Religion which IS a cult.