I have a problem with indoor plastic chairs (like classroom chairs with metal frames) left outside in the rain for months at my units. They are not made of resin plastic and the surface is noticeably rougher & more deteriorated. I think that they can harbour bacteria much like neglected plastic food containers. There is a possible unfresh smell, and some decomposed plastic seemed to end up on my hands when I moved one.
Plastic does not decompose in nature. Decomposition as per my understanding is a phenomenon wherein an object is broken down into simpler constituents. Plastic just breaks down into smaller pieces of plastic. What you are seeing is most probably erosion of the surface due to rain.
I think that they can harbour bacteria much like neglected plastic food containers.
Nothing to be worried about. That chair was most certainly covered with microbes even before you put it out in the rain. Your body itself harbors about as many bacteria as it does its constituent cells.
What it may harbor in addition though are fungi, which now have a great substrate to hold onto.
There is a possible unfresh smell, and some decomposed plastic seemed to end up on my hands when I moved one.
I don't know what you mean by unfresh smell. If you mean moldy, that can be expected because you have moisture, and a nicely eroded thingy which can act as substrate for stability.
You can very well use the chair. There's nothing wrong with it. Spray it with a shower and keep it out in the sun for a day or two, that should take care of the mold.