maybe someone with more RF knowledge than me can help answer this. As a race director, if we aren't requiring alternating right hand and left hand polarized antennas is there any RF reason why we should allow linear antennas at our races?

My thought process: My understanding is that if everyone else is running right hand there isn't really a situation where a linear antenna would interfere with a neighboring RH circular polarized antenna more than another RH antenna would.

Does that sound correct to everyone?

Correct.. except... a Right-hand neighbouring a Right-hand will interfere more than a vertical (what you call linear) neighbouring a Right-hand... but there's only a fraction of a dB in it...