Plexiglass is safe as long as there's plenty of ventilation. You'ld want lots of holes for ventilation and to attach perches, and probably a standard wire top for extra ventilation and hanging toys. It has some downsides though: it's very expensive, it can look messy faster, and it can eventually get scratched up and look bad. Also the birds can't climb on it for exercise, so you would need a slightly larger cage than you would if it was wire, and plenty of ladders and swings and things to climb on. But, less mess makes its way out of the cage which can be nice.
I made a travel carrier with some plexiglass sides - it's small so I used 1/8" plexi and that's still quite expensive. A big cage would need to be made of thicker plexi or it would sag under its own weight... it's not the easiest material to work with.