It depends on which routine, how badly it changes and why it changes.
I've forced myself to deal with all routine changes with my job since they just aren't under my control and when I feel like things change too much over there I just chant "you're doing this to get money, you're doing this to get money" to myself in my head, make it a necessary evil. I've gotten quite good at this, actually.
However, changes to my routines in my personal life are harder to handle since I'm an adult living alone. By all logic, I should have my life under my control... but sometimes mom calls and says she'll be here in twenty minutes even though it's time for me to go to the library. Or dad's at the door even though it's time for me to work on my fictional stories on my laptop. Or when I'm preparing for a weekend backed with my own plans on friday after work and then mom calls and starts to pester me to go to their place for the weekend... usually I just say no, though. I've told them over and over again to inform me at least the day before, preferably more than that, if they plan to come over or want me to go somewhere, but they just don't learn, especially dad.
Of course, not everything is their fault. I had trouble when the grocery store I mainly use closed down for a month because of renovation. I have trouble when the library is closed because of holidays on days that it normally wouldn't be. I have trouble if the grocery store doesn't have everything I went there for (or I forget something) and have to go again to get the missing stuff. I have trouble if I can't go to my morning walk on my days off since it's raining cats and dogs (well okay, I usually still go, it's just much shorter than it should be.)
Then there are bigger things that are breaks in my routines, but I've planned in advance. Big things, like going to visit someone or going to a doctor, cause me huge stress as they are but if the arrangement is made before hand it's not that bad for my routines. Just this morning I arranged myself a doctor's appointment for next monday and am already stressing about it, especially since it's in the middle of the day so I won't be able to relax all morning.