why does the reaction between silver nitrate and sodium chloride have a minimum conductivity well above zero, while the sulfuric acid?

In the reaction between silver nitrate solution and sodium chloride solution, the products are silver chloride precipitate and sodium nitrate solution.
AgNO₃(aq) + NaCl(aq) → AgCl(s) + NaNO₃(aq)
The minimum conductivity is attained when the reaction is complete. At such moment, the reaction mixture contains sodium nitrate solution, which dissociates to give mobile sodium ions (Na⁺)and nitrate ions (NO₃⁻). The mobile ions can conduct electricity, and thus the minimum conductivity well above zero.

In the reaction between sulfuric acid and barium hydroxide solution, the products are barium sulfate precipitate and water.
H₂SO₄(aq) + Ba(OH)₂(aq) → BaSO₄(s) + 2H₂O(l)
The minimum conductivity is attained when both the reaction is complete. At such moment, all the reactants are converted to barium sulfate precipitate and water. There is no mobile ions to conduct electricity, and thus the minimum conductivity is zero or nearly so.

The conductivity of the resulting solution is indicative of the concentration of ions in solution:
Consider the reaction:
AgNO3(aq) + NaCl(aq) → AgCl(s) + NaNO3(aq)
The final solution will contain Na+ and NO3- ions. It will conduct an electric current

Now consider the reaction:
Ba(OH)2 (aq) + H2SO4 (aq) → BaSO4(s) + H2O(l)
The resulting solution has no dissolved ionic compounds - only water. There are no ions present to carry an electric current .