I've been thinking about this question for a while ... Let me compile my thoughts and the comments offered by native English speakers.
According to Cambridge Dictionary
a style that is popular at a particular time, especially in clothes,
hair, make-up, etc.
a new development in clothing, make-up, etc.:
on trend: fashionable
According to Oxford Thesaurus
fashion, vogue, style, mode, craze, mania, rage
According to The Free Dictionary
go out of fashion and go out of style
to become unfashionable; to become obsolete
So gramatically and semantically, it may be correct to infer that you can use go out of fashion and go out of trend indistinctly. But the second one is not used.
Let me establish a paralelism with the Spanish language.
We've got two words: moda (fashion) and tendencia (trend) whose meanings are equivalent to the English ones.
We say that algo ha pasado de moda (something has went out of fashion) but we don't say that algo ha pasado de tendencia (something has went out of trend).