If we’re talking about M+, yes, healers should contribute with damage, and if they don’t people should respectfully let them know how to improve.
M+ is a high performance / speed based type of content in which everyone needs to do damage, no exceptions. It’s literally about how fast you can do a certain dungeon and that means damage (in addition to doing your job well in other areas).
If you’re a Healer and you go to a M+ keystone and can’t bother to press your buttons, then you’re being disrespectful with everyone’s time.
And this comes from someone who’s been a healer since TBC (and even a bit in Vanilla).
In other types of content, specially if the group outgears it, sure, healer damage can be negligible and maybe even irrelevant.