Many people unfortunately clump together things such as asparagus, which may be hard for some to digest, with foods that are actually TOXIC such as chocolate and avocado (as well as others).
Those who wish to "play it safe" and put everything questionable on the toxic list reduce the credibility of that list. If one is to say asparagus is bad and chocolate is bad we don't want those who feed plenty of asparagus to suddenly think "well, she seems to handle asparagus just fine, maybe they're wrong about chocolate too."
So, asparagus - not toxic and not a danger to their lives like some foods. But not all birdie tummies will handle it very well.