Foreign? Huh?
Are you calling some sort of xenophobic insurance companies?
The MINI is completely approved for sale in the US, so it should be just as easy to insure as any other "foreign" car - a Canadian-built Firebird or a Mexican-built PT Cruiser, or a Korean-built Hyundai. Perhaps these insurance companies are behind the times and have not yet updated their computers to recognize MINI as a brand of car - a manufacturer. If you supply a MINI VIN their systems will probably indicate it is a BMW made in Germany, but even so, they should be able to provide you with a quote.
BTW, my MINI is insured through Allstate.