The actual bill text lacks the sensationalism of the linked article. Main objections cited in the bill are the potential threat to privacy of a national DB, the cost of implementation, no clear indication of what the standards for the Real ID would be yet, etc. This item is a bit strange:
WHEREAS, the mandate to the states, through federal legislation that provides no funding for its requirements, to issue what is, in effect, a national identification card appears to be an attempt to "commandeer" the political machinery of the states and to require them to be agents of the federal government, in violation of the principles of federalism contained in the 10th amendment to the U.S. Constitution, as construed by the United States Supreme Court in New York v. United States, 488 U.S. 1041 (1992), United States v. Lopez, 514 U.S. 549 (1995), and Printz v. United States, 521 U.S. 898 (1997);It seems that same argument could be applied to any Federal program implemented at the state level, such as welfare, Medicaid, etc.
There's also the stupid item that other states have opposed it, so Montana should too.