Transition to HTTPS may have some negative impacts on the website’s SEO. After moving to HTTPS you can face the next problems:
- Google crawlers remove URLs with 301 redirects from the index;
- Google crawlers index new URLs.
Speed Https Optimizer extension for Magento places 301 redirects from HTTPS pages to HTTP but only those which don’t contain customer data. It means that you can use HTTPS where it’s necessary and save your Google positions.