Trying to keep third parties off the ballot while still operating under a first past the post system is very different from opposing a switch to something other than first past the post.

Under systems like ranked-choice, IRV, etc., having the Green party or Libertarian party on the ballot would be much less likely to harm the near-term prospects for candidates from the two major parties: most of the voters that minor parties would gain are people who currently pick a major-party candidate that has a real chance of winning. Those voters would mostly continue to select a major-party candidate as a second choice.