Antacid tablet is acid?
You can do your experiment. The active ingredient in most antacids is bicarbonate, and bicarbonates are amphoteric: they can be both acids and bases. In most cases, bicarbonate is a weak base, so despite your bromothymol blue outcome, bicarbonate is a much weaker acid than $\ce{HCl}$, and you should be able to do your titration.