If you are talking about clear acrylic plastic, I think I can help. It only needs to be strong enough to resist snout-bashing, if it's well machined (sawn and drilled). Few iguanas, if any at all, ever bash against the clear glazing on the front of their cage. They run back and forth along it's length, bashing the solid wood sides.
So IMO that's the only level of toughness the Plexiglass needs for Iguanas. So I personally would feel safe with 1/8 inch acrylic, but would still choose 3/16ths. 1/4 inch gives a minimal IMO advantage as it is stiffer, and lays flatter, causing less distortion caused by curved glazing.
In case you don't know, and what the sellers repeatedly don't feel like disclosing, is that plexiglass needs special tools. The drill bit needs a special point angle so it doesn't crack the plastic. The screw/fastener holes need to be over-sized, and the fasteners need to stand short of touching the glass. Saber-saw blades need to be special. The normal sawtooth shape melts the plastic, causing it to bind and crack. Circular saw blades need the special tooth design too. Acrylic cracks seemingly at will with the wrong tools. But well-made plastic panels last a long time, and can take a surprising amount of pounding as long as the edges are not ragged or being chipped. The best edges are sanded smooth (not hard to do) and have an application of acrylic glue to the edges, being careful not to allow any drips. But if you can use 1/4 inch, go for it!
When they get foggy from using paper products like paper towels for cleaning, they can be easily polished back to brilliant clarity. Call Tap Plastics. You might have to search nationally to be able to talk to a good sales person about availability and possible substitutions.
Honest, I don't have any contacts with the plastics industry. I know this stuff because of all the habitats I've built. The alternative is tempered glass, which to me is marginally worth it. Although glass leaks heat both ways much more quickly than Plexiglass, and Plexiglass very noticeably lowers the loudness of outside sounds, both of which whicth (sp banging head on table) I think are a plus for iguanas.