I have asthma that is tree pollen triggered, and we're just coming into my allergy season. Hasn't started yet … fingers crossed it may not be a bad year. I'm also lucky enough to own a turbo (bought last year) and have space for it and to quite enjoy using it. So I'm moving to 100% indoor cycling for the time being. If I do feel breathing problems coming on I can stop immediately. As we move into summer and the asthma risk drops I'll reassess that.
My bike is also a bit damaged, and the fact that I can't just pop out to the LBS to get a new wheel and other parts means it'll likely stay that way for a while. But it's turbo-worthy.
It's depressing, but inevitable, that these circs will be used by the usual suspects as an excuse to have a pop at cycling in general, as is the case with the police quote above and the meme going around that if you go outside on a bike you are highly likely to end up taking up a bed in A&E because riding a bicycle is highly a dangerous activity, like base jumping or cave diving.