Is the core issue that council websites are using real-time bidding for their ads? Is this specific to the UK?
Yes. These websites are used to support a variety of public services, e.g. disability, poverty, drugs, or alcoholism services.
Brave believes that sending tracking information about people accessing this information is a breach of privacy.
The alarm does not come from the technology being uncommon, it comes from these sites being uncommon. In particular, there aren't many sites which millions of people may rely-on/be-directed-to in order to exercise their rights (e.g. to healthcare and social services), or even for their life or their friend's/family's.
The argument of "if you don't like it, don't use it" doesn't apply here. It's especially egregious that these sites are built and operated using public money, so we're paying for it regardless.