Mostly agree with the above. The main issue relates to the depth of the rims center well (spoke channel). That well depth is what allows the smaller diameter tire bead to lift over the side of a rim. So you want to use the thinnest rim tape possible. Personally, I consider well depth a primary factor in rim selection and will not use rims with limited or inadequate well depth.
Before pulling out the tire lever, push the tire to one side of the rim all the way around, then working in both directions, massage the tire around to have the most slack in one place. The goal is to make the round tire take an egg shape so you can work the pointy end over the rim.
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Since you ask about tires --- yes, there is variation. While the bead diameter is standardized, the build up below it isn't. Any material under the bead costs you slack when mounting, so observe and feel this when making your selection. IME tires with a thin visible cloth wrap under the bead seem to easiest to work with. Tires with thick molded sidewalls that wrap under the bead are the worst.
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Last edited by FBinNY; 01-28-23 at 06:10 PM.