I was contacted by @puckipedia regarding the 16-25 railcard website asking for gender. I took a look and found this rabbit hole goes a bit deeper than I expected, with different railcards having slightly different forms, despite looking like just rebrands of the same website. In all cases, gender and title cannot be modified on the website, and you must phone the railcard company to get title or gender changed (as I did a number of years ago for my 16-25 railcard). Note that digital railcards do not include title.
I emailed National Railcards on 15th February 2019 to request a justification for requiring a binary gender on three of their railcards (16-25, 26-30 and Senior). Following a few email delays and some discussion, as of 28th March 2019, I'm pleased to confirm that National Railcards no longer require gender for any of their railcard application forms! Thank you to the Data Protection Team at Rail Delivery Group for discussing it with me and making the change.
Update 2nd September 2020: In these trying/unfortunate/fuwa fuwa/difficult (delete as appropriate) times, it pains me to have to put bad news on this site, but it turns out that Railcards do get a sex value off you if you apply with a passport. Your passport has a machine-readable code at the bottom that contains various information to be read quickly by a computer. There's a breakdown of this information on Wikipedia and it turns out that Railcards will store sex as part of this information and requires M or F to be there. However, the machine-readable passport standard (ICAO Document 9303) states that the character that represents sex can be "M", "F" OR "<", with "<" officially meaning "unspecified". When using a passport with "<" as the sex to apply for a railcard, you get an error message as can be seen in this Tweet by Q. This does make me wonder if driving licenses have the same issue. I will contact Rail Delivery Group to find out more.
So, here's the list:
These are managed separately to the main railcards website and I don't know all of them, so if I miss any please let me know.
I contacted Railcards for an explanation, and they were apologetic about the situation and passed on my comments "for future consideration". I will be monitoring the railcard websites periodically to see if they make any changes regarding this and will report any changes on here.