If your train has been removed from the timetable due to industrial action but you hold an advance ticket for it, what are your rights if you need to travel and therefore a refund and not travelling is not an option. Does the operator still have an obligation to get you to your destination? Should ticket acceptance with other operators be in place?
The Chiltern Railways website is, probably intentionally, rather vague.
Your rights are exactly the same as if the train had been cancelled for any other reason.
The first port of call is that you may take an earlier or later train that complies with the route or company restrictions on your Advance. As a special "easement" during industrial action, you can usually also travel at a similar time up to one day before your booked travel date, and in most cases up until a few days after the end of the industrial action.
If you still want to travel on your booked date and the cancellation means it's impossible to get to your destination in accordance with the route or company restrictions on your Advance, then NRCoT 28.2 is engaged. This requires both the TOC that you had intended to use, as well as any other TOCs that could assist you (e.g. because they run services you could use instead), to arrange ticket acceptance or to accept your ticket as necessary to complete your journey by alternative services.
If it's impossible to complete your journey by train, then NRCoT 28.2 further requires any TOC that's reasonably able to assist (e.g. they manage or have staff at the station where you're waiting) to provide you with alternative transport (e.g. a bus or taxi), or overnight accommodation if that's not practicable.
I should point out, however, that the above is merely the legal position. It doesn't necessarily mean that vindicating your rights will be as easy or straightforward as it should be; indeed, it might be necessary to pay for alternative transport or accommodation out of pocket and then to recover these costs from the TOC afterwards. Before incurring any expenses, it would be advisable to get clear evidence of a refusal to arrange/pay for this - e.g. written correspondence from the relevant TOC (this could come from contacting one of their social media channels, for instance).
Railways are not obliged to provide transport when there’s industrial action. You are advised to check before travelling to make sure it isn’t cancelled.
This is a common refrain but I'm afraid it's simply not correct. But it clearly suits the TOCs for people to think that it's the case!