I had a book recently where I could not change font types. What worked for me on this particular book was when doing the conversion, I think I was doing epub to azw3, on the Look & Feel > "Styling" tab, there is an option at the bottom to "Select what style information you want completely removed:". Put a check in the "Fonts" box.
So, try it?
edit: I'm assuming you are using calibre?
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