I would like to create a rule with a trigger like this:
when a card with the "blue label" with the "{black || sky || lime || pink} label" is added to the board...Or, in more descriptive psuedocode:
When a card with the blue label that also has the black OR sky OR lime OR pink label is added to the board...
It's not super clear but seems like this should be possible given this description from the Butler maintainers:
In conditions that match the name or description of a card, or the name of a list or label, you can use a "wildcard" (or more than one) to match variable text...
Taken from here: https://trello.com/c/jgWL5gAb/214-condition-reference