If you use perfect tuning the 5ths are a slightly larger interval than the way modern instruments are tuned. If you were to tune a piano to perfect tuning based on the key of C, the key of G would be slightly higher than what we hear today. The leading tone back to C would be slightly higher and "lean into" C a bit more. But if you decided to try to play in a distantly related key (say C# or something like that) the spacing between the notes would be so far off that you'd probably need to retune the piano.

Bach wrote the Well Tempered Clavier with a fugue and prelude in every major and minor key. It was a celebration of tempered tuning which meant you could play in every key without needing to retune the instrument when switching to play a piece in a different key.

Put simply, well tempered tuning means that if you walk up the circle of 5ths starting at C, then G, then D, etc. When you eventually get back to C, it will be an even doubling of where you started. With perfect tuning when you get back to C, you'll be higher than that.

But my parent was talking about 12 tone equal temperament?

I replied using a comparison of 12-TET, to scales with unequal steps. The post I replied to, used only the perspective of modern keyboards when talking about transposing music.

You wrote "Modern tuning with 12-TET is not perfect, but good enough, and doesn't yield very dramatic differences when transposed" and I was trying to figure out what differences you were referring to as still being there in 12-TET. As in, why write "very dramatic" instead of "any"?