Think of it this way.
Reduced thrust(ATM) is an attempt to use the minmum thrust required to take off in the distance available. You could have a thrust level that will put you at 35/15 ft at the end of TODA in the OEI go case or stop you at the end of ASDA in the OEI stop case. Therefore anything that may compromise the performance should restrict the use of ATM. Anti-ice fluid will to some degree compromise your aerofoil and therefore its safer to use more thrust that required.
It's a somewhat simplified explanation but I hope it helps.