`DefaultNewInlineCellStyle` only make effect for new generated inline cells.

for example
    
        Cell[TextData[{Cell[BoxData[FormBox[RowBox[{RowBox[{"f","",RowBox[{"(","x",")"}]}],"","=","",RowBox[{"a","",FormBox[SubscriptBox["f","1"],StandardForm],"",RowBox[{"(","x",")"}]}]}],TraditionalForm]],"DisplayFormula"],",",Cell[BoxData[FormBox[RowBox[{RowBox[{"g","",RowBox[{"(","x",")"}]}],"","=","",RowBox[{"r","",FormBox[SubscriptBox["g","1"],StandardForm],"",RowBox[{"(","x",")"}]}]}],TraditionalForm]],"DisplayFormula"],",",Cell[BoxData[FormBox[RowBox[{RowBox[{"h","",RowBox[{"(","x",")"}]}],"","=","",RowBox[{"s","",FormBox[SubscriptBox["h","1"],StandardForm],"",RowBox[{"(","x",")"}]}]}],TraditionalForm]],"DisplayFormula"],","}],"Text"]

Here, for some reasons, $f(x),a,f_1(x)$ in Notebook are not in an consistent style. And Choose them, set same font/ clear format/apply an stylesheet does not take effect. 

If I 

    SetOptions[$FrontEnd,DefaultNewInlineCellStyle->{"Section",FontFamily->"Mathematica",Background->"Red"}]

How to make the prevous inline cells,or futher, all inline cells in the notebook to the new style and formatting.