Suppose, for the sake of argument, the article was about a natal woman who'd been repeatedly misgendered for whatever reason - do you think the absence of (perceived) 'male privilege' would mean everyone would say 'oh, that's all right then'?
Well as I stated clearly, I am not sure I agree with the point being made, I was simply explaining it.
In either case, I think very few people would say “that’s all right then”, but I think you’re still missing the point, which was about men being believed more than women, and is wholly unrelated to the response of the customer service men and whether their reaction was acceptable or not.
My personal suspicion is that fewer women would query a transman with a similar story, especially if they didn’t appear to be taking testosterone. On the balance of probabilities, I’d say a very tall male who claims to be a woman is more likely to have been aggressive and perceived as a potential threat, thus triggering an aggressive response from the other man (reasonably or unreasonably, depending on how polite you feel customer services personnel should be when faced with aggression) than a female who hasn’t had testosterone.
But that’s fairly nuanced and more related to understanding male and female behaviour patterns than about privilege, or lack of it. In other situations, men are more likely to be listened to and taken seriously.
To ask a related question, how many times have you seen articles about transmen being misgendered, complaining about it and being featured in newspapers? I suspect there is some related sex-based privilege going on.