If I publicly distribute posters about a party in my apartment and leave the door unlocked, do I still have the right to kick out anyone I don't like?

That's a pretty diengenuous strawman.

A more accurate comparison would be that you put up an advertisement on a billboard along a busy street and then decided to tell people who passed by that they weren't allowed to take a picture of it.

And to continue with this absurdity you feel entitled to enforce who can or can not look at your billboard because despite it being publicly viewable its your advertisement on the billboard.

That's also not accurate.

There is no "public space" on the Internet.. There's no un-owned territory or resource that is free to use or metaphorically "stand around" in to take those pictures from.

You are consuming privately-owned resources in all your online activities, and as such some will argue that they can decide to limit your consumption of those resources at their own discretion.

Again, I am not siding with either party here, just trying to dispel this notion that "public space" - in the way we understand public space to exist in the physical world - exists on the internet.

In your example, no one is controlling your right to take photos or stand around and look in any direction you choose.

When you use the Internet, a private entity is allowing you to transit through their network and access sites, a different entity is allowing you to access and receive their content, etc..

LinkedIn owns the server you are accessing when you (or others) go to their site, and they are spending resources servicing those requests, and - they claim - can decide how and when they choose to do that..