In some cases there are compatibility issues with other plugins. Most of the time this is caused by another plugin blocking the mixed content fixer. The following plugins appear to conflict with Really Simple SSL:
Plugin Organizer Updating to the latest version of Plugin Organizer should fix the issue that other plugins are disabled after switching to SSL, but before migrating, set the switch in the Plugin Organizer setting „On“ where it says „Ignore URL Protocol“
WP Social SEO Booster: hasn’t been updated in three years, so wouldn’t recommend to use it anyway
USM Premium: USM support appears to have a fix for this, or they may fix it in the next update
Genesis Toolbar Extras, thanks to Jon Burr for reporting it
SEO WordPress (not to be confused with Yoast, which has no issues with RSSSL) output buffer issue, should be resolved in SEO wordpress. Author does not respond.
SEO Pressor SEO Pressor flushes all output buffers, including the Really Simple SSL buffer. They should only flush their own buffer.
GD Booster, thanks to Shane Blevins for reporting it
Deactivating these plugins should resolve your issues with Really Simple SSL.
If you encounter any plugin compatiblity issues, please share this the comments. In most cases, the problem is that the output buffer is used in a way that is not compatible with Really Simple SSL. For example, in the case of USM, the output buffer wasn’t started properly in some cases, which caused the flushing of the output buffer to flush the Really Simple SSL output buffer.