That isn't speech, that's trespassing. Or would you like people to be able to freely visit your home without your "interference"?
On the other hand, union representatives are free to speak to employees outside the workplace; that's speech. (And freedom of association, for that matter.)
An OSHA inspector is a government official, performing inspections in the course of their duties to ensure compliance with health and safety regulations; they can only do so as precisely prescribed by said regulations. Along the same lines, it isn't trespassing if the police come to your home with a warrant in accordance with due process to investigate a possible crime.
Neither of those serves as precedent to allow a random non-governmental person access to private property for any other reason.
So its just a matter of phrasing. If I were to create a governmental body responsible in assisting labor unions in communicating with workers. Then such a representative could be granted that power?
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.)
On the other hand, union representatives are free to speak to employees outside the workplace; that's speech. (And freedom of association, for that matter.)