Actually not true. Most of the ultra orthodox are exempted from service and are a huge source of the support for continued military operations. Because they don’t have to actually put themselves at risk.
It’s been the primary source of netenyahu’s ability to stay in power.
That's the "minor" exception I mentioned. But, as you must be aware, there is also a strong political campaign in Israel to remove this exemption. This is also likely to be a major political issue in the upcoming election.