In “The [Widget], the [Wadget], and Boff, Sturgeon mentions in passing a plethora of alien civilizations and lifeforms, including “fluorine fellowships.” Alliteration aside, the likelihood of a lifeform being based on fluorine in any significant way is very slim; the likelihood of an environment having free fluorine in it is so close to zero that I’m saying it’s impossible. Fluorine will burn water, so the most you could get would be hydrogen fluoride, and that will etch glass, so your putative fluorine world would need to be free of silica. Good luck on that one.
Chlorine, on the other hand, seems more likely. It’s actually a bit less electronegative than oxygen, so it isn’t obviously less likely to exist in a free state. But an atmosphere of chlorine has a serious problem: sunlight.
Chlorine photolyzes all the way down to yellow light, the chlorine molecule splitting into two chlorine atoms. And chlorine atoms are really promiscuous, especially to hydrogen. While they won’t strip hydrogen from water, they will do it for any hydrocarbon, including methane, as well as molecular hydrogen. So you’re really talking about an atmosphere of hydrogen chloride, i.e. intensely acidic.
We use chlorination as a disinfecting process for drinking water and swimming pools, with the latter getting a lot more chlorine than the former. Anyone who has ever had to maintain an outdoor pool can tell you that a sunny day can chew up your chlorine mighty fast. There’s a trick you can use to get rid of the chlorine taste in over-chlorinated water, which consists of just putting the water in a glass jar and leaving it in the sun for an hour. Then you can make your coffee or tea from it without the chlorine taste.
Part of the chlorine in swimming pools goes to hydrochloric acid, which will acidify your pool. We used to use sodium hypochlorite at the old YMCA pool where I was a lifeguard, and the sodium took up some of the acidity. Nevertheless, we sometimes had to add some sodium carbonate to the mix.
Chlorine doesn’t just kill bacteria though; it chews them up and grinds them down into small molecules, including ammonia and organic amines. Then you get chloramines which are even more toxic than chlorine itself. A substantial part of the “swimming pool smell” that most people think of as chlorine is actually from chloramines. For us former life guards, a little whiff of chloramines (or even Clorox) triggers memories.
A “chlorine producing photosynthetic algae” like the one mentioned in “Tranquility” and in Steve Gillette’s World Building articles (and book), probably wouldn’t affect a planetary atmosphere very much, at least at first. But it would begin killing sea life pretty quickly, in a kind of “green tide.” Depending on how it sequestered the alkali elements (I had in mind carbonate in a silica diatom shell), it would also raise the pH if the upper water layers. That would disrupt the carbonate-bicarbonate balance of the sea surface, releasing CO2 into the atmosphere while also depleting surface CO2 as the biologically sequestered carbonate precipitated down the water column. Oceanic primary productivity would plummet, while atmospheric CO2 would skyrocket; a combination of global climate change and a die-off of oceanic life that I figured as apocalyptic.
But of course no one would ever do so foolish a thing as to tamper with the global environment just out of curiosity, or while trying to make a buck, so I'm sure we're safe from this particular danger.