Does not violate one man-one vote

This is a common misconception. The term “one man, one vote” comes from Supreme Court cases about district size. The cases involved unequal district sizes so that the weight of the vote for people in a less populated district was much greater than the weight of the vote for others in a more populated district.
The U.S. Supreme Court made the “one person one vote” rule explicit in Reynolds v. Sims (377 U.S. 533). The rule stated that no vote should count more than any other so that it has unequal weight. This unequal weight would violate the Equal Protection Clause of the Constitution.
This has nothing to do with the voting method itself or forcing people to use our choose-one voting method, plurality voting.

Voters using Approval Voting may not vote more than once for any candidate. The existing ‘design and construction’ of ballots, both paper and electronic, do not permit voters to vote more than once for any candidate or issue.

Proponents of Approval Voting do not seek a change here.
No candidate shall receive multiple votes from a single voter,
as is current law.

Colorado’s newest party is seeking citizens of the state to register to vote as Approval Voting Party members.

The Approval Voting Party has been established in Colorado. On October 1st 2019 over one-thousand Colorado voters have registered as AVP which was founded in late 2018.

The second statewide convention will be held in Denver on March 1st 2020.

Voters naturally want to choose more than one.