A mouthwash with chlorhexidinedigluconate, lidocaïneHCl, mint spiritus, glycerin, alcohol and water gives a cloudy

The turbid is simply due to the interaction chlorhexidine + and Cl-with formation of the insoluble chlorhexidic hydrochloride.  

You can therefore best replace the lidocaïneHCl with Benzocaine 40 mg per 100 ml of mouthwash