The Constitution does not say that the tariffs cannot be protectionist in nature, nor does it define what protectionist is. All it says is that it must be applied uniformly throughout the country.
And on the subject of protectionism, the Morill Tariff as passed also placed significant duties on molasses, raw cotton, sugar, tobacco and tobacco products, and naval stores. All items that the south produced in quantity. Did not the Morill tariff provide a protectionist safety net to the south as well?
You've got it backward: The Constitution does not authorize tarrifs that are 'protectionist in nature' unless they fall into one of the mentioned categories:
1. Pay debts.
2. Provide for the common defense and general welfare.
The Whigs (and the Republicans that followed) had no pretentions that the tarriffs they would impose had to do with either of these things. The Constitution musn't just not prohibit something, it must specifically authorize it.