A TOC is not just like any business (large or small) because (barring open access) they are operating under a franchise agreement.
They are required to provide a particular service level. In many cases they are paid to do so.
How does it then make sense for them to be able to arbitrarily refuse access to their services?
As
@Krokodil notes, like all businesses, TOCs are subject to an extensive legal framework prohibiting unlawful discrimination. So long as they are complaint with this, any business can theoretically exclude whomever they want. But why would they!? It doesn’t make sense to
prevent them from doing something they would never do in practice.
Why do you imagine that TOCs are more likely to
arbitrarily exclude people than other businesses? Have you got any examples of where this has happened!? On the other hand, specifically
because they provide a service to the public, there are good reasons for TOCs to be able to exclude individuals who behave in a threatening/dangerous manner.
Again, you seem to have a strange paranoia about the railway being out to get you!