The Responsive theme has a custom home page option, with a feature content div that is defaulted to an image. I cannot get shortcode for my slideshow plugin to work in this. I can insert html just fine, but no shortcode. Also, major noob here.
I suspect this is going to require a theme edit.
I am assuming that your shortcode is visible on the front-- something like
[gallery]-- but not processed as a shortcode. If that is the case, you will need to find where that content is output in the theme and pass it through
do_shortcode before echoing it. That could be more or less difficult depending upon how the theme is written.
If the shortcode does not make it through to the front page at all, then I have to assume that shortcodes are stripped from that content when it is saved. That is a tougher fix and would require more information.
It is possible that the theme has a hook you can use to avoid a direct theme edit.