While fierce might seem to go with debate better than with disagreement, "fierce disagreement" is used.
- By the mid-1980s, everyone knew something had to be done. But just what
to do and how to do it became subjects of fierce disagreement.
As to the substance of the alleged debate — whether or not it is a core tenet of Islam that believers must wage holy war against non-believers wherever they are found — there is fierce disagreement on that issue even among acknowledged experts in Muslim culture and theology, so I will not attempt to defend one side or the other in this brief commentary.
With so much agreement, the stumbling block was fierce disagreement over whether airports or airlines should be responsible for the assistance at airports.
And what role does this meaning play in the code? We have several millennia of fierce disagreement as to _every_ core issue of meaning.
The field of developmental instability has generated a large amount of controversy recently, mostly because of fierce disagreement over the genetic basis of fluctuating asymmetry and its role in mate selection.