As Irene2805 said, for 2020 you are a part-year resident of both states and as such are going to only be taxed on the income earned in each. You will not apply the credit for taxes paid to ID in MT as there is not income that is being taxed in both states in 2020. You can only apply the credit for taxes paid to another state if the income is taxed by both jurisdictions.
Which is exactly what occurs going forward. Montana taxes on your total Federal income which includes all the Idaho income. You will prepare Idaho non-resident returns and Montana resident returns. You will claim a credit on your Montana return for taxes paid to Idaho for the income that both Idaho and Montana tax.
Montana Form 2 Credit for Tax Paid to Another State or Country Schedule
