Earlier quoted context omitted.
What's the concentration of that vs the concentration here. Note that we also use chlorine to treat drinking water (e.g. on canoe trips), but you don't want to be drinking that unless it's very low concentration. A quick google search suggests that they are used to "improve water clarity" [0], so at a guess you don't use enough of it to turn the water pink. There's also the fact that they think it's concentrated enou…
I would not use livestrong as a source. If the pictures are true to the situation, the concentrations are tiny. You can look up videos of people putting less than a teaspoon into water to get the same result. IIRC, PP can be a precursor to chlorine. But, you're comparing two different chemicals here and what applies to one likely doesn't apply to another. There is a chance your skin will feel like it's burning if it'…
Converting KMnO₄ to Cl¯ would require a nuclear reaction. Chlorides are generally soluble, so it's not going to cause an insoluble salt to slowly dissolve as a permanganate salt precipitates instead. It does appear to be a stronger oxidizing agent than Cl₂ (and Cl¯ and ClO¯ and ClO₂¯), but there are likely better reducing agents in most water than dissolved chlorine ions.