Yes, from my (limited!) understanding it's fairly easy for those states to make oil drilling economically infeasible. The easiest way is to simply ban any pipelines from the ocean to the shore, meaning all oil produced by the platform would have to be picked up by ships.
This is yet another example of a very disturbing and ongoing trend in US politics however, where states and the federal government are becoming more explicitly adversarial. You definitely saw some of it coming from the states in the past as they tried to sabotage the ACA but that policy was at least implemented evenly on a national level. (if anything it actually helped the sabotaging states more on average, but I digress) Now we appear to have national policies being enacted to explicitly favor/disfavor states based on their partisan identification. Attacking your political enemies through policy is unsustainable for a functioning democracy but I don't think conservatives realize that. Could get ugly.