Hi Ruben,
Thanks for using Shortcoder. It could be that the theme is overriding the background color on the page wherever the shortcode is inserted.
Since shortcoder does not manipulate the content, there is no way shortcoder can strip off the styles. If background color is the only style which is not working then it is definitely a theme styling/overiding issue. You can confirm this by adding other styles like font color, size etc.
If theme is overriding the style, then you need to inspect the style or check with the theme/plugin author and see how to reduce the specificity of the CSS style.
Hope this helps.
Thanks,
Aakash