Ever since Blogger added that option to Stats, years ago, it's been a problem for some blog owners. Sometimes, the problem is individual, other times (as this year) the problems are seen by more people.
The most common problems with the "Don't track" option, when selected by the blog owners, involve cookies, hosted by various browsers - and interpreted by Blogger scripts. Cookies and scripts are misunderstood features in Internet life.
Some countries require websites, published by their citizens, to display disclaimers, warning readers that "This website drops cookies onto your computer!" - as if cookies are are part of an evil plot.
Every security feature or product, installed in a browser or on a computer, contains some cookie and script filters.
Every security feature or product is subject to updates, by the provider. Many security features and products update automatically, without consent of the computer owner.
Whenever Blogger code is changed, we see reports of problems from some filter, that's part of some security product, located on various computers. Sometimes, the security products, updated automatically, detect problems with Blogger code - without any changes having been made by Blogger.
There are hundreds (possibly, thousands) of different security products - each provided by a different company, and each updating their filters separately from the others.
The problem is complicated by various details.
- Ongoing activity - maintaining Blogger code, to keep it compatible with newer browser releases.
- Current activity - upgrading Blogger code, to provide SSL (aka "https") connectvity.
- Ongoing problems - some computers shared by multiple people - and some people use multiple computers.
It's not a given, unfortunately, that Blogger will be able to make any one change, to make this problem go away - immediately, permanently, or universally. Please consider the epidemiology and history of Blogger problems, in general.
That said, if your problem is purely from a blocked third party cookie, you may be able to workaround the problem, by creating the cookie, manually.