This is a tough situation, on the one side I agree with
@BuzzH in that the whole point is to fund wildlife in the first place and that you should apply at your own risk... as always.
On the other hand, if the state closes a season and there for makes it impossible to use a service you bought from the state I think that's a problem that needs to be remedied.
Personally, I think a fair middle ground would be for the state of Montana to figure out what they are going to do prior to May 11. If it seems that continued measures are necessary or likely to be necessary, to then bar NR hunting before May 11. They should then cancel the non-resident MSGB draws (no refunds for app fees). For elk and deer NR would be allowed to either take an 80% refund as it's before Aug 1st, per the statue, or hold onto their tag and use it for the 2021 season.
I think generally speaking this is kinda what all states should do... cancel and refund the Big 3 and then for elk and deer, allow some sort of refund or a carry-forward policy. All app fees and base hunting licenses would be non-refundable no matter what, you applied in the draw you took the risk. Hunters would be out some money and the state would be able to split the loss between this year and next year (they would subtract the NR who are carrying forward their tags from next years quota).
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Assuming the state decides to cancel seasons and leave everyone out to dry you can always try to do a charge back on your credit card. I think in this specific instance where the state is the denying you access to a good/service you purchased from them you absolutely have grounds not to pay.
I'm not sure what the split is between hunters paying with CCs versus debit cards but I'm assuming it's a pretty high percentage. If 5000 hunters do charge backs at $1000 a pop the credit card companies would have plenty of leverage to get the state to revisit it's policy.