Hi,
Which version of AEM are you using? To add components inside responsivegrid or parsys, it should be unlocked which is correct, if you can drag and drop components inside parsys and component has design dialog with style system then you can apply styles.
Are you applying style to parsys or the components inside parsys? Make sure your parsys component is unlock.
I tried same with responsive grid, works for me.

Arun Patidar

