If you are not sure how your site will behave when upgrading or changing themes, you should create yourself a test/dev site. There are many tutorials out there that can help you set up a local test site.
You can make a copy of your live site and transfer that all to your test site locally.
From your question I suspect that you registered your taxonomies in your theme, which in case, if you switch themes, your taxonomies won’t be displayed.
I would advice you to move your taxonomies and CPT to a functionality plugin using the functionality plugin. or this tutorial. This it according to me the correct way to go, and this will ensure that when you decide to change themes, that your CPT’s and taxonomies won’t be affected.
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