What is the products for HCl + Na2S04 + BaCl2?
BaSO4 + NaCl. The HCl doesn't enter into the reaction.
Na2SO4 + BaCl2 ==> BaSO4 + 2NaCl
Why doesn't it enter the reaction?
Why do reactions occur?
A ppt is formed. BaSO4 in this case.
A gas is produced. None in this case.
A weak electrolyte is formed. It is true that BaSO4 is more soluble in acid solution (due to the formation of HSO4^- ion) but other than that, it isn't part of the precipitation reaction. If you want the formation of the HSO4^-, it is
H^+ + SO4^- ==> HSO4^-
However, that reaction occurs to such a small extent that for all intents and purposes it doesn't occur UNLESS you are precipitating BaSO4 as part of a quantitative process for determining Ba^+ or SO4^=, THEN you must worry about the small extent to which it occurs. I hope this is clear enough.