J. - I know that this may seem like a go-to answer to some on this site, so take it for what it's worth. But please know that I'm not trying to project my situation on yours. I just want you to have the information.
I have a child that is a high-functioning autistic (you likely wouldn't realize it if you met him) and those kinds of issues are common for him. He has to be the first in the door, must have the same songs sung in the same order before bed. Things that counter his routine are difficult to process. He is quick to temper and slow to let it go. He used to have tantrums that would last an hour, sometimes striking out. When something doesn't go his way, he gets immoderately upset and resists our attempts to talk him down from it.
These reactions are common to a few related problems and frequently get ignored because these children look and (mostly) act like everyone else. I also have a child who is typically developing just 14 months behind and the difference in how they handle these events is apparent.
Having stated that, you are right that a certain amount of reticence to change is normal at this age. But you might consider having your child assessed for sensory processing issues, autism spectrum disorders, OCD, ADHD or something else in the same neighborhood. (What is the harm in just checking it out?) It could be that what is making her anxious is that she doesn't experience her surroundings the same way that most of us do.
Hour-long tantrums are not typical and having problems with having things moved, someone else's change of shoes as well as acting out added to that doesn't seem like anxiety. I would think that rather than anxiety being the diagnosis, it is likely that the anxiety is a symptom of something else.
It takes a team of people to diagnose these things properly, so please keep that in mind before taking one person's word: whether it be one doctor, one therapist or one (this) mom! I would seek an opinion from a team qualified to do it as it is really key to start any therapies early.
Finally, if nothing else I wrote is useful, I use the book 1-2-3 Magic with both of my children and it does seem to help both of us because it takes the emotion out of the discipline process (keeping me sane) and helps my kids learn how to regulate their own behaviors. I find, though, that discipline has to evolve with them.
Again, take all of that for what it's worth. Best of luck finding the right answers for your little one.!