Wow. The TL;DR of this seems to be that on the TRA…
folded, bagged bikes…you’re in.
non-folding, bagged bikes…maybe.
non-folding, non-bagged bikes…roll the bones.
FWIW, what do they have against any part of the bike being exposed? Sounds rather specific.
The info on that Taiwan in Cycles seems to be outdated, or at least contradictory to parts of the TRA website, and other sites that show people with non-folding, road ready, unbagged bikes latched to poles in the cars.
I thought the Taipei MRT allowed bikes to be rolled on in certain stops and cars (first and last cars, I believe).
The TRA station where I live has a 10cm strip on the side of the staircase to roll your bike up and down. The lady behind the counter showed me a list of what times I would be allowed to take my bike on the train. Of course, I am guessing this means an unbagged non-folding bike can go on the train. Usually, only local trains stop here. No luggage facilities that I am aware of.
That said, any look up of trains will not pop up with the bike icon on the schedule.
It would be great if it was just simplified to “all unbagged bikes allowed except during certain times and only in certain cars.”