Can't advise on CA specifically, but in my experience insurance policies offered as benefits with group membership are 'insurers of last resort' - if any other insurance (like your own household policy) could possibly cover you for the incident, then the group policy won't pay out. See for example things like the 3rd party liability offered with Dogs Trust, BHS and others.
Depends on what you want to insure against. There is probably no insurer more experienced in the issue of countryside crime and the hate crimes associate with it. If you hunt regularly the only insurer that will back you if you are accused of an offence, attacked on social media, threats made to your employer etc is Countryside Alliance. As a basic 3P insurer - BHS offers high limits. Personally we have both!