A better example might be that your right to a jury trial conflicts with my right to freedom of movement, but the government explicitly resolves that contradiction by making it a crime to avoid jury duty.
What about the victims' right to justice and to be secure against violations of their rights (bodily integrity and health, property, freedom of movement and flourishing)? If there are no judges and all the criminals are left to roam the streets, they are free to continue victimizing anyone they choose. Seems to me that these rights have a lot of mutually incompatible features. You can't provide for one person's rights without compelling action from another.
That happens, you believe?
https://www.cbc.ca/news/canada/british-columbia/canada-jorda...