You are entitled to your opinion however the railway is entitled to decide they do not wish to allow any individual to be a member.
They are certainly not under any obligation to allow someone to volunteer. Even if the risks of allowing a member with a criminal record were small, they may consider the risk of reputational damage to be too great.
There is also the possibility it may cause concerns, bad feeling and resentment among other volunteers and employees; the organisation may not want to risk losing other volunteers.
If you had kept a low profile then you may have not had an issue, however anyone with a Youtube account that includes videos of a concerning nature does risk being denied access to opportunities.
I do multiple jobs but in the job I did today, if anyone had a Youtube channel such as yours wishing to do voluntary work with me, they would be barred from doing so. And if I asked that particular employer if such a person could do voluntary work with me, questions would be asked regarding my own judgement.
Someone who had a troubled past but was working to change their outlook and was no longer publishing views that were likely to be contrary to those considered acceptable by a preserved railway, may well be viewed in a more positive light.
It is the railway's call and you have to accept that. Some people may sympathise with you but I doubt anyone with any relevant experience is going to state the railway has acted incorrectly or outside their remit.
Also in your opening post you state membership may be "best avoided"; I agree that in your case it is best not to challenge their decision and to forget about it and move on.
However in contrast, I would say that there is no evidence that membership of the railway is "best avoided" for anyone who does not publish videos of the nature you publish and who does not have a criminal record.
This post is not intended to have a go at you, but you have posed the question and therefore the above is my honest answer.