In general, going out will be interpreted as "go (out of my house) to a place where people have fun". I can go out eating (to a restaurant), go out dancing (to a club, or when you are my age, a disco), go out drinking (to a bar).
As a general statement, this is the only common interpretation: the sentence describes a habitual act, not a specific situation.
Context changes everything though:
I was in the room, then I went out (,)dancing.
Means indeed I went out while, at the same time, I was dancing: I cha-cha'd my way to the door, I waltzed out of the room, I quickstepped out or I tangoed into the hallway. In that last instance, obviously I am not the only one leaving the premises, because, as J.R. notes in the comments, it takes two to tango
I love to go outside dancing.
Describes my liking of actually going outdoors to dance in the open. (No, I don't do that, really.)
After I insult everybody in the room, I love to go out dancing.
This is ambiguous, but the mention of the room indicates I may actually leave the room while showing off my sense of rhythm to the insulted. It could also mean I like to go to a club after the insults are delivered. Unless you get to know me better, you can never be sure...
"He is gone out" is not idiomatic English. It treats "gone out" as an adjective or other description of state. This is not usual.
"He has gone out" is normal present perfect construction. It is saying that, at some point in the past, he went out. Usually, this means he's not in at the moment, though it will occasionally be used when he's already come back - though "he has been out" is more usual, then.
Both contract naturally to "he's gone out", which may be a source of confusion.
If you want to use a descriptive present tense to describe his state, given that he's gone out, you use out as an adjective: "he is out", or contracted to "he's out".
n.b.: You will find "he is gone out" and similar constructions, using is instead of have for the present perfect, in older texts. It was once a normal thing, but hasn't been for some time.
Best Answer
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
fashion
trend
and
According to Oxford Thesaurus
trend
According to The Free Dictionary
go out of fashion and go out of style
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).