"degree of sincerity" is correct and usable in written English.
It is an expression that expresses the intensity of sincerity. For example: "I could tell by the degree of sincerity in her voice that she was telling the truth."
Gardiner is less than thrilling in the role, but he possesses a degree of sincerity.
It would be unseemly and ultimately impossible to decide the degree of sincerity in individual cases, the judge suggested.
Tillman once described himself to me, with an indeterminate degree of sincerity, as the best lyricist in the business.
Even more so, it calls into question the degree of sincerity of fear over Cold Start as expressed by Pakistani military leaders to USG officials.
If these same people had been exposed from early youth to great masterpieces of literature and had learned through them to appreciate the tremendous diversity of human mores and beliefs held by other groups, with the same degree of sincerity that they themselves possess, they would be less likely to be as harsh, intolerant, and rigid as they are.
(Will we be eating flash-fried insects, she asks with a certain degree of sincerity and what may be prescience).
Most of a day's idle conversation is a sequence of thumbs-up, thumbs-down assertions expressed with varying degrees of sincerity and conviction.
In fact, the Ayatollah, who had his own website (http://english.bayynat.org.lb/) epitomised what Western critics, with varying degrees of sincerity have been suggesting Islam should be.
The protesters further lack the political experience and organization to effectively influence powerful political groupings that have their own agendas and governments who embrace their demands with varying degrees of sincerity.
