If you want to protect the privacy of your readers to be respected you won’t have much choice but to create your own website, and store it on a privacy respecting webhost whil using non privacy-invasive techs to manage your blog.

For example, I use Hugo (a static website generator, but there are other similar tools), without any script running on the website itself. So, there is zero tracking going on on my blog (I don’t even know if anyone is reading it unless they decide to send me an email, as there is no web contact form either). It’s hosted on a small host that I’ve been using (& trusting) for well over a decade. Hugo itself is 100% free, but the webhost rarely is. So, unless you know how to self-host you will have to pay a little something (you don’t need much to host a simple blog, unless you want to post video?).

Like suggested in another comment, if you just want to limit access to the content, any simple ready made solution allowing for password-controlled access should do the trick.