Chlorhexidine is intended for local use only. From PubMed Health:
This medicine may cause serious and permanent injury when placed in the eyes, ears, or mouth. Carefully follow all instructions before using this medicine to prevent these serious side effects.
Martindale: The complete drug reference, 34th edition lists the following potential side-effects:
- multiple episodes of cyanosis and bradicardia (in an infant whose mother sprayed her breasts with chlorhexidine when breastfeeding)
- mild giddiness, unusual laughter, and an increased appetite (in an elderly lady who mistakenly drank 30 mL of 4% chlorhexidine)
- gastritis (mistaken ingestion)
- pharyngeal oedema and necrotic oesophageal lesions, increased aminotransferase concentrations and liver necrosis (150mL of 4% solution)
You may say that the concentration of your solution is lesser than in most of these examples. The quantity, however, that you intend to use is much larger. Even though you probably intend to use it over a prolonged period of time, not at once, the fact that chlorhexidine is not intended to be ingested remains.
Edit: As rumtscho has pointed out in comments the tax may be significantly lower because the liquid might contain other ingredient(s) that make it unsafe to drink. Bottom line is that if something is not intended for peroral use, it should not be ingested (even if you find a way to remove chlorhexidine).