Answer by Rabbi Chaim Hillel Raskin – Rov in Kfar Chabad Beis, Israel:
Min haTorah, the prohibition of basar bechalav applies only to milk and meat that were cooked together; yet midrabanan, we scrupulously avoid any form of mixture between meat and milk.
The Rema quotes that it is customary to have separate salt dishes for milk and meat because food is sometimes dipped into the salt and it might contain food remnants that are milchig or fleishig
The same would apply to otherwise pareve spreads because an unclean knife may have been dipped into them.
Although this concern doesn’t apply to a salt shaker, it is still important to have designated salt shakers for two reasons: (1) Food can get stuck to the shaker, and (2) taste can be transferred to the salt when pouring it onto hot food which has steam yad soledes bo.
Based on these concerns, one should be careful to have designated containers of salt, sugar, ketchup, and the like. If the same container is shared for milchig and fleishig, one must be cautious not to pour directly onto milchig or fleishig food, and one shouldn’t touch the cover with dirty hands.
Shulchan Aruch rules that if bread is touched by milchigs or fleishigs, it may not be eaten with the opposite type. As a precaution for this, if one ate dairy and now wants to eat meat (or vice versa), in addition to cleaning the table and changing the cloth, he must remove all leftover bread pieces from the previous meal out of concern that this bread has residue of dairy or meat and thus it may not be eaten with the opposite type.
Nevertheless, eating such bread on its own doesn’t require waiting afterwards like actual dairy or meat if there is no noticeable residue for the concern is only doubtful.
Poskim explain that if one had a loaf of bread or challah on the table, the concern is only on the slices that he cut to use during the meal, but not on the remainder, if it was kept clean.
Likewise, if one had a bag of sliced bread on the table, one need be concerned only with the slices of bread which were taken out of the bag, but not the slices that he kept inside the bag. If there are young children by the table, one may not use even the remainder of the loaf with the other type if they may have touched it with their dirty hands.
Published in the Weekly Farbrengen by Merkaz Anash. See sources
That is why on Shavuous you have 2 meals – eat milchig, bentch, wait and wash again for fleishig.