I think that much depends on how a term is used (as always with language). Of course it is ok to refer to older people ('grannies' is arguably a different matter, though) in a discussion about differences in internet access. When talking about the propensity to click on links however, unless you are saying that older people are less likely to do so (a generalisation at best) then why bring age into it? The word 'grannies' is not neutral in that context, if ever it is, really - it's both dismissive and reductive.
The two things (internet access and willingness to click) are not remotely comparable. For one thing, everyone on here is, by definition, IT literate, or at least able to operate an Internet browser, and for another, I can't see why someone's grandparent status would make a difference to whether they click links or not, any more than their age would matter. Is a 40 year old 'granny' more or less likely to click on a link than an 80 year old who is childfree? Who cares?
It is very lazy to assume that people are motivated to do things by their generation. I explained my own motives for clicking or not clicking upthread, but others will have different ones. I have had the same basic rule since I was in my 30s and first started doing a lot online - if in company (including on the train or bus) the sound is off, so video links have to wait and stand less change of being viewed unless they are work-related in which case I make a point of watching them later. If a link is to a long article I may or may not have time to read it when I see it, as I am often working when online. Again, if I don't have a burning desire to follow it up later, there is a good chance that it will be missed, as the moment of relevance will have passed.
Also, people are warned about clicking links in case they are dangerous. I have stopped embedding links for that reason. I realised that people prefer to be able to read the url to see what is coming, so now show the whole thing, even though it spoils the look of a post. I'm not particularly cautious personally, but it's only polite to recognise that many people see things differently.
I have seen a lot of snide digs at older people on here lately. Ageism is the last acceptable prejudice, and I'm surprised that it is still tolerated, particularly on here, as GN is supposedly a safe space for the over 50s.
(and I agree that using 'culture wars' as an excuse for denigrating others is tedious, too)