"goes contrary to" is correct and usable in written English.
You can use it to express that something is opposite or in opposition to something else. Example sentence: "The government's decision to raise taxes goes contrary to their commitment to reduce taxes."
It goes contrary to everything we're doing.
Mr. DeMint's grievance, though, goes contrary to Mr. Bush's vision for the program.
"It goes contrary to the spirit of trying to reform the Legislature," he said.
"To the extent that the book goes contrary to that, I think it is unfortunate," Varghese said.
"The imposition of new American economic sanctions goes contrary to the spirit of interaction and cooperation," the Belarus Foreign Ministry said in a statement.
But the idea that Clinton would quit at this juncture goes contrary to every single thing we have learned about her over the past 17 years.
"So much of the world is going contrary to the ideals of Passover".
"We're going contrary to state laws," said Bill Swenson, one of seven former mayors of Longmont who fought the ban.
He saw it as a form of musical prostitution, but much of his output and other people's output under those conditions turned out things that go contrary to what you would expect.
He said the extremists systematically destroyed cultural heritage because it went contrary to some of their doctrines, but also because "heritage is a source of funding for extremist groups".
"It does seem to go contrary to what the whole point or the whole purpose" of the sex offender registry is, said Steve Conlon, an F.B.I. official and former assistant director of the Iowa Division of Criminal Investigation who previously oversaw the state's sex offender registry.
