If you just want to display something on a web page, no, it probably doesn't matter, although it probably should.
If you actually want your colors to look right when you print on a digital printer, it is absolutely important.
Here's an interesting video showing soft-proofing on Affinity Photo-- even if you don't use Affinity, it's worth watching, because it does a very good job of demonstrating why color spaces actually matter.
https://www.youtube.com/watch?v=Lb8_yxRK7gA
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