Home Improvement

It could be a couple of things that I am aware of.

Dust would be the most obvious. Many plastics can hold a static charge and dust can stick to it. The pattern looks "splotchy", so if not static electricity, it might be oils or some other kind of chemical that is mildly sticky. (Injection molding can sometimes use release agents during manufacturing that are rarely cleaned off. Don't eat random bits of injection molded plastic, kids.)

Simple moisture could be the issue as well. If you have been using your air conditioning, it'll get the plastic cold and water can condense on it. Dust or something else might be sticking to it. The water could dry, leaving behind the dust and obfuscating the root cause.

While it could be a mold of some kind, it doesn't look too much like it. That would point to existing mold in the ducts that is sporulating. Those kinds of house molds are usually dark and nasty, not white. White house molds exist but I suspect it's region specific as to what kind would grow where you are at. (I grow mushrooms, so I have a supply of petri dishes I would test that substance on, TBH.)

Just for good measure, check your air filters. It's something you need to do anyway and if they are nasty or old, you could be circulating excess dust in your house and it's a sign the filters need to be changed. Air filters are functional! Air conditioner heat exchangers can get clogged and, depending on the type of unit you have, be somewhat costly ($500-$1500) to clean properly. I have paid for this procedure twice before I found out that the air filter assembly is garbage in my unit.

Is the substance oily or powdery? If you clean it off, how long does it take to come back? Did someone spill something near that register that you weren't aware of? Were the carpets recently cleaned?

I am sure that HVAC people may have a more direct answer, but that is my list of things to check.

It's the splotchy pattern that is bugging me though. It's highly unlikely that something is getting sprayed out of the air ducts, other than small quantities of water condensation.

OT: The stain in the middle looks like a little froggo <3

Does the stuff scrape off? What’s the result look like if you give it exactly one good scrape with a flathead screwdriver?

Call a tech and get your heater serviced. Yes you're supposed to get those looked at annually. When they're doing your heater, ask them what they think.