It's not the snare stand, it's sympathetic vibration. Change the tuning on the toms and the snare to widen the gap in the note each drum is vibrating at when hit.
Also, it goes without saying, make sure that NO part of the snare or stand is resting against the kick drum, as that can often make it worse.
You may also want to try tightening up the snares themselves, but it's going to most likely be sympathetic vibration. Get the gaps in notes bigger, and that will lessen the effect. You'll most likely still have some, and like jaybriggs said, if you have the drums individually mic'd some gating will help out a lot as well.