I'm trying to do a single color Musgrave texture, like transforming the white part of the Musgrave texture to be transparent, is this possible to achieve? Attach with an example https://blend-exchange.com/b/BJj3qdx6
This should do it - Just connect the inverse of the texture to the Alpha of the Principled BSDF.
However, since this is a Musgrave texture, which has values that go below 0, you must add a clamp node first, otherwise the invert will not work the way you expect. I also suggest adding a ColorRamp Node because there is still a thin white outline around the edges due to interpolation, which can be cut off rather easily with the ColorRamp slider. Don't forget to change your Blend Mode to Alpha-Blend or Alpha Clip, if you are using EEVEE.