seriouslyffs I say that because OP said that her gran is 'sheltered' and 'naive' and not nasty.
If she was saying things in front of children I'd probably say something like: 'Oh, come on, Nan!' Once children get to about nine, perhaps even younger, most of them are capable of working out that though we love people, sometimes they say stupid things.
I put sheltered and naive in inverted commas because I found that description quite insulting and ignorant - though maybe it's true in her gran's case, she knows her better than me.
My mum would have been 92 if she had lived and was far from sheltered and naive. She held liberal social and political views and had friends of different creeds, colours and sexual orientation. Yay, my mum. What a cool old woman.
Yet she did worry about the threat of Islamist terrorism. Not for herself, because her life was nearly over, but for us.
The worrying thing for her, and OP's grandmother is of the same generation so may share the same fear, is that in what she described as 'her' war, Britain was more homogenised and the enemy was an outsider who was easily identified.
That belief may have been an illusion - and she certainly did not believe that someone who was not the same colour or faith as her could not be her friend.
But on the occasions she expressed opinions that I disagreed with, I did not 'pull her up' on them. I may have told her that I disagreed and explained why in a discussion.
But 'pulling someone up' speaks of an attitude that is hectoring and the opposite of tolerant and, like Moonatic said, whiffs of virtue-signalling.