You can change the protection on the shapes to prevent resizing.
Of course that will lock them in their current size. You will need to delete the text first to return the shapes to their original size. This could be a lot of work, but Visio has a concept called Masters. Masters live in stencils. When you drag a shape from a stencil to a page, you are dragging a master to a page and that is creating an instance of the master on the page. If you change a master then you decide if all the instances change.
An alternate is to create an empty stencil. drag the shapes you want to the page from their stencil. Set the protection on these shapes. and then drag these shapes to the news stencil. You now have a stencil that does not resize.
Of course, the lazy way would be to be less verbose with the shapes text, something I find hard to do. Reducing the font size sometimes help, but then you are back to your original problem, inconsistencies, but this time in
text.