From Halachically Speaking by Rabbi Moishe Dovid Lebovits
The Rama says that the minhag is to have separate salt utensils for
meat and for dairy. The reason is that some food particles remain when
the food is dipped into the salt, and one may inadvertently mix milk
and meat.The poskim say that this halacha applied in the times when
salt was placed in open utensils. Today, however, we use saltshakers,
and this reason does not apply. Therefore, two separate saltshakers
are not necessary. When children are in a household, one should have
two separate saltshakers, since they stick the saltshaker into the
food. [Ed. Note: If one pours salt from a shaker into a hot meat or
dairy food cooking on the fire or just removed, it is best to use the
shaker only with that type of food.] Some are careful to always have
two separate saltshakers. If one puts salt from a fleishig saltshaker
on dairy food or vice versa, (even when there are children in the
household) then the food may be eaten. It is best to try to remove the
salt from the food.
This is based on Rabbi Yisrael Belsky Shlita, Kaf HaChaim 31, Badi Hashulchan 88:31, Rivevos Efraim 5:514, Yalkut Yosef page 346, Piskei Halacha Kashrus page 25:21