To many people, a computer is simply a tool and as long as the layout is similar and the basic features are there (browser, e-mail, word processor etc) it won't really matter that it doesn't look exactly the same as the one they used before.
The problem is that to many people, a computer is simply a tool and if the layout is different in any way from what they're used to, or the basic features aren't where they're expecting them to be, they assume they don't know how to use it and give up. I assume this is the difference between being computer literate and rote-learning
[1] an interface. A bit like the people who'll only drive Fords because they can't get the hang of other manufacturer's dashboard layouts.
If they're not too resistant to learning how to use what is for them a *completely different* computer, you can teach them where things are and they should be able to get on with it, but may need hand-holding through every unexpected difference.
It's not really about Windows vs Linux, anyway. Anything that causes a change can be a problem, from a OS upgrade that massively changes the GUI paradigm (Ubuntu being notiorious for this, but now Microsoft are just as guilty) through routine software updates that rearrange the menus of their mail client, to someone moving the icons around on the desktop.
[1] My anecdotal experience is that the rot set in with GUIs for the rote-learners. There was a time when you could give them a cheat-sheet of keyboard commands, and they'd be happy.