I offer these reflections for what they're worth, and I'm not sure how much that really is. Technical caution concerning oil paint, though, is probably a word to the wise.
There is concern over the use of Zinc White in oil, particularly in the lower layers or priming of a painting. In fact, it's always been obvious that Zinc White in the underpainting is a bad idea, because it's an extremely slow drier - and the last thing you want in paint over which you're planning to add layers is slow drying; not only does it hold you back, it also increases the risk of the paint film cracking later.
The new concern - or relatively new - is to do with the formulation of metallic soaps, areas of instability in the paint which can cause delamination: in other words, can lead to the paint just lifting from the canvas and falling off. Zinc White is far more likely to form these soaps than other whites, like the traditional lead white, or at least forms them much more quickly. But Zinc has been mixed with actual painting grounds, the so-called "gesso" surface on which one paints; it was also mixed with some lead whites, and it was assumed that this was a sound enough practice (its intention was to make the paint more workable and less prone to yellowing) since the negative characteristics of Zinc would be overcome by, eg, Titanium, or lead.
There are now question marks over this, which have come to the fore over the priming of artists' canvas. That priming is usually acrylic these days - but there are those who suggest that this is still a potential problem. I simply don't know if they're right or wrong.
Unless you make your own sizing and prime your own canvases with the material of your choice, and none is without drawbacks, any canvas or canvas board you buy is likely to be primed with an acrylic paint containing Zinc; it won't be pure Zinc, but will be mixed in proportion to Titanium White; the latter should be the major constituent, but looking at my own Daler-Rowny container of acrylic gesso, there's no information on it to give any sort of clue as to its composition. So - this is not likely to cause any problem with acrylics. I don't think it's very likely to cause any problem with oils either - but to achieve the longest life possible for your paintings, oils should be painted on rigid panels rather than flexible canvas: one of the best would be canvas glued to wood or other rigid boards. Canvas, which is easily damaged anyway, is very prone to being affected by climatic conditions, temperature, humidity: these factors can hasten the deterioration of oil paintings, cause cracking, promote the creation of metallic soaps.
Acrylic on canvas seems a much safer bet.
Is this worrying too much? Perhaps it is - but even so, in any work I'm offering for sale, I now avoid Zinc White, which I would never have used in priming products (knowingly) or early layers anyway; and on the whole I use rigid panels rather than stretched canvas for oil painting. Keeping an eye on these technical questions can make one extremely neurotic - and the lack of certainty makes it worse. But at least if you know there are potential issues, you can make up your mind how to respond to them, or whether to respond at all.
And in the meantime, here's my landlady's 86th birthday card, from an oil sketch; and it's true, you wouldn't know she was 86 (if she'd only wear her hearing aids...).