Do you know what isn't creepy and privacy invading? Analysing the attributes of the visitors to FranksKebabShop.com, as part of the tooling that runs FranksKebabShop.com.
This could be analysing web server/cache logs. It could be a more active piece of software that operates via JS and reports back to a service running on the same domain.
I know, I know "everything is SaaS now, nobody installs software". Nobody can install it if you don't make it installable. Be part of the solution not part of the problem.
I personally wouldn't use one that isn't OSS, but plenty of people don't care about that, but do care about privacy, including the privacy of their site visitors.