Some xylitol is fermented from corn, while some is fermented from acceptable sources. Unfortunately, the corn-derived version is the most popular, probably because its' cheaper.
I personally won't consume it because I need to be extra careful with my diet. You need to decide for yourself how compliant you want/need to be. Also, what kind of vinegar is in the ketchup? Any other questionable ingredients?
I do occasionally buy xylitol gum for the kids, since only a tiny amount ends up being consumed and most of the xylitol stays in the mouth, where it can be helpful for oral health (it feeds good bacteria and starves bad bacteria in the mouth.) If I were to purchase xylitol, I would use it to make mouthwash, not to bake with.