Most (all) people have internalised at least some stereotypes and fall prey at least a little to most (all) of the series (sexism, racism, ableism, homophobia transphobia, classism,...) They may be aware of this, and consciously try to go against those internalised beliefs, but nobody is completely free from prejudices. Sexism is just one of the more noticeable ones, as sexist beliefs dictate for everyone what they can and can't do, and it's impossible to avoid as it's present everywhere.
Ableism, homophobia, transphobia, on the other hand, are only directed towards a subset of the population. It's perfectly possible to go your whole life without ever meeting a trans person or being confronted with trans issues. In that case, it's possible to never show any transphobia, regardless of what you'd do or think if you had met a trans person. This makes transphobia a lot less present, less visible, easier to pretend you don't hold those beliefs or participate in continuing them, easier to pretend it doesn't exist.
Sure, there are people claiming sexism doesn't exist, or that it does exist but they're not part of it, but sooner or later sexist thoughts and/or actions will be present around them—whether they (allow themselves to) recognise them or not—and they'll be most likely to hear about it from the women they know. Contrary to trans people, it's impossible to go through life without ever meeting a woman (women are still the primary victims of sexism; male victims are often ignored or not believed).
In short: I'd rephrase languagepotato's quote as "All people are sexist, some less, some (especially men) more."