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Yes, it's completely normal - your brain prefers what it already knows, so any significant change triggers a natural alarm. What matters is whether you can recognize the fear and take a step anyway, not whether you don't feel it at all.
Fear of change is human, but what I've noticed is that often the idea of change is scarier than the actual change itself. Once you really start, you discover it's not nearly as bad as you feared! The trick is not to overthink it beforehand, because your mind plays tricks on you when you have time to dwell on it.
I think it depends on whether you're forcing the change on yourself or it's being forced on you without a choice. When I had to change something in my daily life for a serious reason, I was afraid but the fear was smaller than the feeling of "I have to do it anyway"; when I think about changes I could make but I'm not sure I really want them, that's when the fear becomes huge and paralyzes me. The difference is that in one case you act, in the other you're just stuck with the anxiety.
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