[Just_Harry]

My mother cleans schools for a living, and she once remarked to me that most of the teaching staff in the grammar schools[1] she cleaned would avoid making conversation with the cleaners, and some would even avoid making eye contact, which was contrary to non-selective schools, where most of the teaching staff would make conversation with the cleaners.

[1] Grammar schools are academically-selective, state-funded schools in the UK and elsewhere—staff and students alike are generally of a higher socioeconomic milieu than in non-selective, state-funded schools.

[s1artibartfast]

Is that what people mean by lack or respect?

Seems more like disinterest or a lack of friendliness.

[Just_Harry]

Not initiating conversation could be down to disinterest, yes.

But I think consistently refusing eye contact does constitute a lack of respect, if the person refusing to return eye contact has no problem returning it to the upper echelons of staff. And, having attended one of those grammar schools, I know that some of the teachers who refused to return eye contact had no issue with faux friendliness.