Do you remember art classes at school? There would frequently be a need to put newspaper down to protect surfaces against some mess, and every so often, the paper would turn out to be The Sun - with it's Page 3 model. Back in the 1980s, this would cause a little excitement among the boys, and a huff from the teacher who didn't think we were ready for life drawing classes yet.
I'm reminded of this every time I have to mask a bit of layout with newspaper and then take a photo for a magazine. You need to be so careful, as readers will work out what you've used and judge you for it.
No point in sticking a copy of Socialist Worker in front of them, even if it's nothing more than a peripheral part of the photo. You'll be able to hear the sound of subscriptions being cancelled...
My solution is either a local paper, or in this case, some old pages from Private Eye, Once without any swearing, or contentious stories on, just to be sure. Ideally, no photos either - someone will get offended.
I suppose I ought to buy some rolls of brown paper, the stuff used for masking up cars for painting, but it's just another thing to store, and I don't need this that often.