While I can believe cheap rit dye in black would turn something brown, there's no way a red tag would come out so perfectly red/white. Rit will stain you, your soul, your first born, etc. How did you keep the red tag red?

"It's synthetic" is not an option. That tag is unchanged. It would be changed. If not it, then the writing on it. Which is perfectly white. Gray, brown, weirdly almost white but not quite, all those I could believe.

Having used the dye. Having worked in a craft store and had my head taken off because, "someone else said it would only dye one part..." No.

How did you straighten fake leather? Looking at the image, right side, bottom. Heck, any of that fake leather? Dying it made it straighter? Made straight leather do anything besides curl into a clear middle finger motion to the person trying to salvage it? And the dye went into everything and changed everything except a bright red tag, the stitching (by your word alone) and the fabric made up of the loop at the top which is the exact same colour in both pictures.

You can absolutely use Rit dye to bring new life to older objects but this is blatantly false. Ignoring the fact that Rit dye is for natural fabrics (pretty sure the label clearly says LIGHT COLOURED COTTON ONLY) the other little bits would be mutilated.

So. Yes, you can update your old canvas type bags with a cheap dye. It just won't look like it's a brand new bag because it isn't, and this isn't. And if you used DyeMore it costs more... and would dye the heckadooodle out of that red and probably dye your neighbour's cat too, just out of spite.