The obvious answer is to find another assignor. I realize that may not be possible in your area, however.
If insurance is your major concern, you do have some options. Purchase the National Association of Sports Officials (NASO) coverage. It is very reasonably priced and covers you for any sport you officiate, regardless of the sanctioning body.
You also mentioned NFHS..If you are a registered NFHS official in your state, the insurance coverage extends to you officiating any sport at any level that is also a sanctioned HS sport in your state.
I would also recommend that you do the research for yourself on these options to make sure they will work for you. Then, you can accept games without having to worry about being covered by a specific association.
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