I have two configurable attributes and I want their selection not to be dependent, as select first option one and then option two.
Is it possible to select the options at any order, thus without any dependency?
Yes it is. Everything is.
But not with the JS magento provides.
The problem is, magento builds a JS which has this way:
so to achieve this you need to change most of the code to create a complete graph which options are possible with the yet made choices.
I wouldn't recommend this. It is a lot of work and if you think about the order, I think most of the problems can be discussed and not implemented.
You have shirts, they have a size a color and a printing.
I think it is clear, that you first choose the size, because for whom you buy this shirt, the size is fixed. The second choice is a business decision but both is right if you ask me.