DefaultNewInlineCellStyle only take effect for newly 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. Choose them, set same font/clear format/apply an stylesheet does not take effect, because of different values of StandardForm and TraditionalForm and other.

If I do the following

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

How to make the previous inline cells,or further, all inline cells in the notebook the same formatting style?