LinkedIn is a private company and a private site, they can do whatever they wish, just like you are free not to use them. If something should be open to all people then it should be managed by the government (who are themselves, at least in the american case, under strict rules about freedom of speech and other things that private companies are not), but LinkedIn is not.
I get the want about being notified when your posts are deleted, but again this is a private company, they aren’t for you, they are for profit.
Now that doesn’t mean that I don’t think something like LinkedIn should be made into a public utility (or something better designed and less profit focused but rather more for helping people), but as it stands right now, it is not, it is a company. If you don’t like private companies being able to do what they wish, since they are private companies, then indeed you are likely anti-capitalist, as that freedom of companies is free-market capitalism in a nutshell.