There is actually a law severely restricting any business's right to determine who solicits and who doesn't on its premises. As a result, unions can organize without permission and under federal protection if Target or Wal-Mart allow any solicitations on their grounds. Blame the federal government's meddling here, not Target.
I wonder if it would be possible for a store to arrange with the Salvation Army to have a store employee ring the bell and collect donations (receiving permission from the Salvation Army to use the appropriate trademarks, with the Salvation Army receiving 100% of proceeds)? If a store did this (at a cost to the store of $80/day or so, which would likely be outweighed by the goodwill such a move could generate) it would totally lay to rest any claims that they selectively allowed solicition since the bell ringers would not be solicitors).