I've had Saigas since ~2000, and have never had the shells deform just loaded in the magazines. I've had some magazines loaded for years and not had an issue.
I'm assuming you're referring to the shells loaded in a magazine that is locked into the gun against a closed bolt. For my factory mag catch Saiga where I have to hook the front and rock the back in, I do find that the top rounds can be squished where they are pushed down into the mag by the underside of the bolt. I don't seem to have that problem in my others where I have custom mag catches where I can rock the mags in front-to-back, back-to-front, or just straight in. I typically insert them rocking back-to-front, so the necessary compressing of the shells on a closed bolt is through the brass rims, and I've not noted a deformation of the hulls then (but I've not left the gun loaded for extended periods as I use it for matches and cycle ammo through frequently). Another way to get around the front squishing is to insert the mag with the bolt locked back so the top cartridge doesn't get squished while rocking the magazine in.
Now, to what you're probably asking - pressing on the front end of a plastic shotshell hull (as a normal Saiga does when inserting a mag) is going to deform the plastic hull. The above poster has the solution for that - use a metal hull. I've got some old brass hulls that I'd probably use if it was a problem for me.