What should I look for in a respirator for chemical processing of photographic materials

In general, don't.

It's far better to ventilate the darkroom than to wear a respirator. Easier on you (respirators are stressful to wear, as everyone ought to know after more than a year of COVID-19), and more effective (you don't have to think about having a second set of exhaust fans if you invite someone in to watch you work in your darkroom or instruct you in a particular technique).

There are few chemicals used in modern photography that would make a respirator preferred over a good exhaust system, and some (those with an ammonia scent, for instance, or which exude sulfur compounds) make exhaust a better protection than a respirator.

If you can't add ventilation, then mix your chemicals outdoors, with the breeze at your back so the dust and fumes are blown away from you -- or prefer dustless and odor-free chemicals in your buying decisions.

Except for the smell of acetic acid, an ingredient in both the fixer and the stop bath, photo chemicals are relativity benign. Some rare cases of contact dermatitis which goes away if usage is stopped.

I personally have worked with and breathed them for more than 55 years. I am 83 and still kicking. Besides, I was a registered environmental assessor, and I say you have little to fear. That being said, you are better off mounting an exhaust fan to expel chemical fumes. Such an installation is tricky because is must not leak light.

You can cut a hole in the drywall (wall) and mount a small fan. You can use one designed to ventilate a bathroom. Drywall walls are usually hollow. You cut another hole, offset from the fan hole. This can be up, down, or sideways. The idea is, you create an exit path for the fan output. The offset is a light trap. The offset must be 1 yard / meter from the fan. Spray flat black paint inside the wall.

If this is too much for you, you can buy an light proof darkroom ventilating fan.

It depends on one's particular needs.

Developer is quite toxic, fixer and stop - not really.

Developer doesn't evaporate anything except water vapor, stop and fixer evaporate some non-toxic (but smelly) ingredients.

Nothing in the process hints that one can get mist of doplets of any of the solutions and inhale them.

Dry forms of the chemicals can create some dust. Not really an issue, but can be irritating.

Now, what do you want to prevent?

• Touching your face with dirty hands? Wear a covid mask (and probably safety goggles).
• Inhaling the dust from the dry chemicals? Wear a covid mask (and probably safety goggles).
• The acidic smell? Wear a covid mask and a cotton mask soaked in sodium bicarbonate solution over the covid mask (and probably safety goggles as well).

There are respirators w/ changeable filters that can help you with the last point.

The first point is really important only if you want kids in the darkroom with you. If this is the case, also bear in mind that some developers smell sweet and are still poisonous.

I agree with the answers that suggest that you don't need a respirator for health and safety reasons, but if you simply don't like the odor of acetic acid or if you are worried about exposure to the point of distraction, then follow the recommendations of the manufacturer as published in their MSDS (Material Safety Data Sheet).

As an example here is a PDF MSDS for Kodak Indicator Stop Bath. Note that there are separate recommendations for the concentrate and for the working solution.

The MSDS says to use ventilation first and foremost, and if this is not adequate, use a respirator with an organic vapor cartridge. This would be the same cartridge as you would use for paints and solvents.

You should be able to find an MSDS for any brand and type of darkroom chemical that you plan to use.