Is it the Na+ or the Cl- that gives table salt its taste?
The salt receptors are sodium ionic channels, i.e. peptides which are selectively permeable for Na ions [1].
Ionic current causes receptor activation and neural responce.

Anion plays minor role here, imposing upon salty taste. The result may appear acidic, bitter and even sweet.
For example, I believe that sulphates are overally bitter.
Carbonates or alkali probably just burn the receptors and may have random taste.