I was able to find one paper noting a transient increase in MDR gene activity in cells upon exposure to Cannabis, suggesting the enzyme may have a role in metabolizing Cannabis. That might suggest a mutation in MDR1 might raise Cannabis levels in the system above what might be expected for a dose, but the paper did not go that far.
I noted on VIN that a dog manifested possible Cannabis toxicity symptoms while being suspected of also having the MDR1 mutation. The dog also had Ivermectin. All the specialists focused on Ivermectin as a possible problem despite the symptoms of apparent Cannabis toxicity. None mentioned Cannabis as a likely cause of problems in the dog, despite the mention of MDR1 mutations.
There is otherwise a dearth of information on VIN on this topic, which probably says something. Given all the above, I'd suggest there is not a contraindication there, but you might want to try the low end of the dose range for any Cannabinoids used, and that if you did so, you'd probably be safe