"fundamentally contrary" is correct and usable in written English.
You can use it to describe two ideas or situations that are very different. For example: "His approach to the problem was fundamentally contrary to mine, and we were unable to come to an agreement."
Torture is wrong and fundamentally contrary to American values.
"Doping is fundamentally contrary to the spirit of the sport," reads the World Minigolf Sport Federation's rule book.
"Suspicionless mass retention of communications data is fundamentally contrary to the rule of law … and ineffective," the Latvian official argues in a 120-page report, The Rule of Law on the Internet in the Wider Digital World.
As has recently been reported, the competition didn't screen participants for performance enhancing drugs – a standard expectation for sports covered by the Australian Sports Commission, which considers doping "fundamentally contrary to the spirit of sport".
Believers in a strong unitary executive branch think the president has the power to remove even independent commissioners – at least when they act in a way that is fundamentally contrary to the will of the executive (and, in this case, contrary to the submitted comments of nearly 4m Americans).
The workshop is a process, an unscripted performance space, a regime for forcing people to do two things that are fundamentally contrary to human nature: actually write stuff (as opposed to planning to write stuff very, very soon), and then sit there while strangers tear it apart.
Solitary confinement is fundamentally inhumane, extremely costly, contrary to the public good, and often unnecessary.
Amnesty's report concludes that the camp closures are a positive step forward for human rights, but the fundamental problems of arbitrary detention remain in China: Many of the policies and practices which resulted in individuals being punished for peacefully exercising their human rights by sending them to RTL have not fundamentally changed: quite the contrary.
But more fundamentally, the researchers have shown that, contrary to prior belief, a class of materials called indirect-band-gap semiconductors can yield practical lasers.
The Israeli-Palestinian conflict is fundamentally a political conflict, and thus, contrary to what Ms. Robinson said, has no place on the agenda of the United Nations conference on racism.
This was something that, in the face of a good deal of evidence to the contrary, I truly did believe, fundamentally, as a matter of faith.
