I'm currently working on a large map art that uses lots of different coloured carpets. I'm building it one colour at a time, so Baritone keeps trying to place carpets I don't have in my inventory, causing it to just stop building. How do I make it only place the colour of carpets I have in my inventory and ignore every other colour?

You can remove blocks from the schematic with buildSkipBlocks. There is no automatic way of doing this for everything not in inventory though.