Since the end of World War II, Minnesota has had four ballot-qualified parties other than the Democratic and Republican Parties. But if the new law, requiring a vote of 8% instead of 5%, had existed in that past period, Minnesota probably would not have had any ballot-qualified third parties other than the Reform Party in 1996-2000.
The American Party became ballot-qualified in Minnesota in 1976 by polling 6.57% for U.S. Senate. It kept that status in 1978 by polling 5.68% for Treasurer and lesser percentages for other statewide race. If the law passed in 2023 had existed back then, the American Party would never have been qualified.
The Green Party became ballot-qualified in 2000, when Ralph Nader polled 5.20% for president, and that status lasted until November 2004. No statewide Green ever polled as much as 8%.
The Independence Party became qualified in 1994, when Dean Barkley polled 5.39% for U.S. Senate. It changed its name to the Reform Party in 1996 and polled 11.77% for Ross Perot in 1996, so even under the new law, it would have had qualified status, starting in 1996, not 1994. In 2000 it changed its name back to the Independence Party. It didn’t have any statewide nominees in 2004, and in 2006 its highest statewide showing was 6.44%, so under the new law its status would have ended that year. In reality it kept its status through November 2014.
Chances are the Independence Party would never have come into qualified existence if the new law had been in effect back then, because its 1994 only statewide showing was under 8%. Ross Perot would still have started the Reform Party in 1995, but when that party went into steep decline after the 2000 presidential election, there would have been no transition to an Independence Party because that party would not have existed as a qualified party.