Runflat tires aren't made out of some magical, technologically advanced material that controls every aspect of your handling. If it was, every tire would be made out of it, because they are virtually the same. A runflat tire is designed to be driven approximately 50 miles at 50mph or less with little or no air pressure "safely". Driving any tire without air in it will cause the tire liner to breakdown and shred from rubbing against itself leaving a lovely smelling ground rubber.
Runflat tires are not designed to support the weight of the vehicle, the air inside them is, runflat tires are designed to have thicker material so that when you drive on them flat they don't immediately shred away and could make it down the road a ways. Several if they are punctured at all are completely ruined because they can no longer fulfill that purpose.
Mixing run flat tires and non runflat tires is not dangerous in the least, mixing performance rated tires or models of tires across the same axle can be dangerous, but no more than having a wheel out of alignment. The weird feeling that people may be experiencing by mixing tires could possibly be related to the difference people feel in running nitrogen in their tires, completely in their heads.