Is 'venerability' a real personal quality or just a social rank or institutional privilege?
It can be both. One might achieve a certain rank in a religious organization which comes with the title "Venerable". Or one might have certain qualities which, together, make said individual the object of veneration: someone might be noted for compassion and charity and develop a following of people who revere said individual for those traits.
What personal qualities do you think makes a person 'venerable' in this sense - what makes them worthy of veneration, revered, respected?
Loving kindness. But that's a personal thing.
Have you known anyone you would look up to as 'venerable' or 'revered'?
Several, to different extents.
If, as the anti-religious wish, society completely abandons religion and spirituality, would it be possible for persons to be venerable or revered in the absence of these cultural traditions? Are there civic or social virtues for which one could be revered or venerated, in the same way that those with spiritual qualities have been in the past?
Well, I'm not sure that human society can do without religion/spirituality. However, for the purpose of this conversation the answer seems to be: yes.
We can take my loving-kindness as an example. Even in the absence of a religious or spiritual tradition, if people find loving-kindness to be a good quality, a quality to be cultivated in one's self, then we can see how someone who exceptionally manifests the quality might be venerated for the attribute.
The only problem is that veneration often carries religious connotations, but the word, to my knowledge, does not necessarily entail religious connotations so I see no problem with this sort of use.