Q:

Can I take a soft suitcase on Qatar Airways?

Are you allowed to take a soft suitcase on Qatar airways I have heard that some airports are starting to ban soft suitcases but I am not sure if this is true or not

A:

In these situations the best thing you can do is check the company rules
https://www.qatarairways.com/en-gb/baggage/allowance.html

Baggage allowances may vary according to route and cabin class; please
  check the exact baggage regulations printed on your ticket.
Baggage guidelines:
Maximum dimension = length + width + height; 
A single piece of checked baggage should weigh no more than 32kg (70lb). Any bags weighing more than 32kg (70lb) must be broken down so that each piece weighs less than 32kg (70lb). 

So only weight and dimensions are taken into account for your baggage, not materials

