Replying to @JibberJim and @LeonieWatson, @ChanceyFleet, @ugly_chimp, @lukOlejnik
I don't think that looking at it in too black & white terms helps. If your access logs are only processed as logs, accessible to a limited group, and have limited retention I would call it fine. The rights and freedoms are okay, as we say.
For behavioural profilers, the biggest issue is that they have access to the same information that allowed detection of a screen reader in the first place. That's scary. Browsers are a huge walking Article 25 violation, they should be taken to task over that.