You can change the DefaultInlineFormatType for "Text" cells to DefaultInputInlineFormatType (i.e., "StandardForm"), and change the style "InlineCell" to inherit options from "Input":
SetOptions[ EvaluationNotebook[], StyleDefinitions -> Notebook[ { Cell[StyleData[StyleDefinitions -> "Default.nb"]], Cell[StyleData["Text"], DefaultInlineFormatType -> System`DefaultInputInlineFormatType], Cell[StyleData["InlineCell", StyleDefinitions->StyleData["Input"]]] } ] ]
Here is screen capture from a notebook, showing a text cell with an inline cell, followed by a normal "Input" cell, so that you can compare them:
