I am 9 weeks pregnant and I’m still using products with salicylic acid as I have acne, and also a mild retinol serum on occasion. This is baby number 2 and I basically gave no thought to what I was using on my face for no1 and she turned out fine.
Technically speaking all retinols are also retinoids, as retinoid just means a vitamin A derivative, however generally in skincare the term retinoid is used to refer to the stronger (ie closest to pure vitamin A) prescription products.
In my view no product that is sold off the shelf in a shop (rather than over the pharmacy counter or on prescription) is going to do any harm, as if a product is able to pass through the skin’s barrier and have any effect it would have to be labelled as a medicine - like the stronger retinoid creams such as trentoin) that have been proven to be dangerous in pregnancy. (This is also why most skincare products claims are likely to be unfounded, but I digress)
And yes salicylic acid is aspirin (I once made some in first year chemistry at uni) and as another PP said some women are prescribed low dose aspirin throughout pregnancy so I can’t see why on earth it would be a problem to use it on your skin.
I really really hate the scaremongering that goes on around pregnancy, which understandably panics many women- like that quote from the end of the study that @EdgeOfACoin quoted. Basically the view seems to be avoid everything and go and lie in a darkened room, ^just in case....^
I’d recommend the book ‘Expecting Better’ by Emily Oster, which looks at the science behind a lot of the common pregnancy recommendations and is very sensible- not sure it covers skincare though.