Framed Drawers can be textured using Mekanism Plastic but it always gets rendered as white Plastic and as Mekanism if i understand that correctly follows forges guide for colored Blocks i am reporting this here and not at Mekanisms Bug tracker.

Used Mod Versions:
Forge 14.23.5.2825,
Chameleon 4.1.3,
Storage Drawers 5.3.8,
Mekanism 9.7.5.376

btw: Drawers are also incompatible with Mekanism Metal Blocks but that is a Mekanism Bug and i opened a PR to Fix that.
Edit: that PR is part if Mekanism 9.7.8 so Mekanism Metal Blocks should work now Plastic still doesn't.

What's the forge guide for colored blocks?

If the plastic blocks use a base texture that is modified by mixing with a color, it probably isn't gonna work. I think the framed drawers only grab the face texture. (Actually, it grabs the particle texture of the block specifically, because that's the only thing that I could see readily available on an IBakedModel). I could try to grab this off the baked quad list, which would expose tint data, but I bet that would give some pretty wild results on some blocks.

What's the forge guide for colored blocks?

I found a guide for that at the time i made this Issue but i can't find it now.
The closest thing i could find right now was mcforge.readthedocs.io/en/latest/models/color.
But i am pretty sure the page i originally found also told people to do that for blocks like wool or concrete.

If the plastic blocks use a base texture that is modified by mixing with a color

That's pretty much what happens and so you can only get white plastic, white plastic road, white slick plastic, white glow plastic and white reinforced plastic as texture for framed drawers.