What problem, precisely, are you attempting to solve? What right, precisely, are you attempting to defend? What makes that problem more important than the rights of a private association of people to their privacy and the security of their property? If you want to argue that the balance between two rights suggests that one right should override another, you should 1) identify both rights, and 2) explain why no possible approach exists that could preserve both. You haven't done (1), and you haven't made any case for a lack of alternatives.
Such communication (unlike the inspection of on-premises equipment and workplace safety, or the investigation of a possible crime) is already readily possible via any number of other means. You are, for instance, already free to stand just outside of such a campus and attempt to communicate with employees there. You can even get a pile of people together with picket signs, and if others agree with you you'll get plenty of sympathy. Employees who are already members of a union are also free to speak to other employees.
You are free to speak; you are not free to force others to listen, or to force others to provide you with a platform to speak from.
Trespassing on a private campus to tell people what organizations they should or shouldn't associate with seems approximately as appropriate (and about as welcome) as trespassing on a private campus to tell them who they should vote for, or to tell them about a product they should buy.
You'd have much better luck getting yet another mandatory notice added to the list of "conspicuously posted" notices, which would serve the same function of communication. On the other hand, what would you even have such a notice say? Those other notices exist to inform people about corresponding laws that exist.
(Strictly speaking, a government can attempt to pass a law giving itself any power it likes. For instance, a government could attempt to pass a law giving itself the power to enter a private residence for some random purpose it thinks important. Such laws can also be overturned by courts in defense of more important rights, such as freedom of association and private property. So saying that "a government could pass a law" doesn't actually constitute an argument.)
(Also worth noting: this entire argument relates solely to an attempt to imbue unions with the force of law and trample other rights in the process; it is unrelated to arguments for or against unions themselves.)