Some of those claims have actually been dispelled by that Snopes link though some of it is true, but the problem probably doesn't lie mainly with the chlorine issue.
"As an antimicrobial treatment to minimize or reduce the contamination of the finished product, cocktail carrots can be treated with chlorine.
Those that are will be subsequently rinsed with potable water to remove the excess chlorine before being packaged." (One should make it a general rule to rinse out all vegetables, etc, before consuming and then hope for the best if you're not then cooking it

.)
"According to the Canadian Food Inspection Agency, the use of chlorine as an antimicrobial treatment is a current accepted practice in the processing for
all ready-to-eat vegetables..."
"As for the '
white film' the emailed alert claims is the 'chlorine coming to the surface,' that white blush is
caused by dehydration of the cut surface -- were you to pull a carrot from your own garden, slice it in half and place it in your refrigerator, it too would manifest that same whitish appearance on the cut portion once the carrot dried out a bit. Cocktail carrots are more prone to develop this only because their entire surface area is a cut surface."
"Generally, consumers can determine whether small carrots are true baby carrots or not by looking at what's listed on the packaging. Labels that say '
baby carrots' appear on packages of very young carrots that are harvested while the vegetables are still quite tiny. Labels that proclaim '
baby-cut carrots' appear on packages of petite carrots made by chopping down and polishing much larger versions of the vegetable."
What concerns me more is that: "...'baby-cut carrots' have been specially bred to contain more sugar than their standard sized cousins because this extra sweetness appeals more strongly to children." And then there's the colouring. Personally, I really don't much care for genetically enhanced or some cross-bred produce. However, I have not researched on how the "bright orange color has...been bred into them..." so, to be fair, it could very well have been done through a very safe and natural method.