I have zero railway knowledge of rostering, but legally, there is nothing stopping an employer from publishing a rota internally for all to see. Indeed, it may even be necessary for operational reasons, or in the interests of fairness, for example, to check that favouritism etc hasn't been introduced.
It is likely to be proportionate and necessary to work in that way. If you had a very specific reason why you did not want your shifts to be published, it would likely need to be on the basis of a protected reason. It is possible that some of your colleagues do have a protected reason.
However, equally, unless it is a term and condition of your employment, there is no requirement for the employer to do the exact opposite. I suspect most of your terms and conditions will be within a collective bargaining agreement rather than your contract of employment.
Legally - in terms of regulation or statute - there is no requirement to publish, or indeed, not to publish.