If your taking it from a glass jar and pouring it into a cup to drink that day there's no issue. That said, while I would fill a sports bottle up once or twice with coke for a few hours, I wouldnt re-use the same bottle dozens of times.
The reason that you shouldn't use most plastic or colored glass to house acidic drinks long-term isnt persay because it "degrades" the plastic but because the acid acts as a solvent and some less than savory compounds (think free-radicals/potential carcinogens) can be freed from the plastic (or the colored dyes in glass) and can enter your drink.
None of this happens in the span of an hour or even overnight, but leaving your Kombucha in one of those containers for a few weeks might not be a good idea.
The thing is that most plastics and glasses are safe from this, but it's often hard to differentiate which containers are safe and which aren't so in general people are told not to use them.
Long story short, the cups will be absolutely fine, and unless you use only one cup, and let your kombucha sit in it for hours on end I dont see you having a problem.