My experience with sharing objects between variants.

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This border becomes thicker if you make a shared image bigger in a different variant.

If you have an image (or anything else) with a border that is shared across variants and “scale line width’” is on, when you change the size of the object in a variant, the border in the other variants changes with it, even though the image in the other variant stays the same width/height.

And yes, you can most certainly argue that that is supposed to happen when Scale line widths is on, but now you have two images of different sizes, yet the border size remains the same between the two.

It seems better to have Scale line widths only affect the variant you are actually working in.
Text can be shared between variants, and you can change the text size (and other styling options) for it and only have it affect one variant.
With border size you seem to only have 1 option. It all has to be the same, regardless of the size difference between objects in variants.

And I know, I know, I could just select “Stop sharing with variants”, which is what I’m doing now, but that defeats the purpose of being able to share between variants for easy editing when you want to change something later.

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I just noticed this is also a problem for shadows. If you scale an image that has a shadow in a variant (which increases the blur amount) the shadow of the image in the other variant changes as well.
This can’t be how sharing objects is supposed to work between variants.

I can see that Know1.

However that's not the way I'd create a border as stroke widths overlay the image, so if you had something silly like a 96px stroke, 48px is outside the image whilst the other 48px is inside the image.

The image is just held within a container shape, rectangular in this case. So don't use a border stroke. Clone the image and using the fill tool change the fill from photo to Flat Fill. Ctrl+Shift+B to send it behind the photo. Adjust the flat fill size to suit your required border. Select both and soft-group. Share with Variant. If you wish you can select the Flat Fill rectangle in the variant and stop sharing that, but the image remains shared.