It's more a matter of courtesy as opposed to "responsibility".
Perhaps if you don't expect them to read it until morning, then you might as well wait until morning to send it.
And if you're getting complaints about your sending texts at midnight, then that should be your cue to not send at that hour.....at least not to the people who've objected.
Very well said, and I am in complete agreement with you.
It is a matter of courtesy, and respect, (and the use of the word "responsibility" in this context is depressingly telling, and revealing of attitudes), respect for downtime, personal space, sleep, and privacy.
Hold off until morning, unless it is absolutely vital; and no, the "responsibility" not to contact someone is yours; it is not for them to have to disable their phone.
Actually, I see the fact that this sort of question is even asked as part of the encroachment (and entitlement) of employers into the "private space" of those whom they employ, a sense that emloyees must justify why they are not always available, or always "on", 24/7, which is something that I, personally, find outrageous.
In general, unless it is an absolute emergency (which, by its very definition, is something that is not a frequent occurrence) I will not text (personally or professionally) at midnight.
In any case, I see this is discourteous, and disrespectful of someone else's time, and personal and private space.
However, my (mobile or cell) phone does not live in my bedroom - it is permanently exiled downstairs, and, increasingly, I leave it behind whenever I head out somewhere, which is wonderfully liberating.