Since you mentioned that you're already building a SPA, I'm going to assume that you have already done your due diligence regarding whether or not SPA is the best approach for you, else I'm with Aleksandra that just because SPAs are the flavor of the month does not mean that they are the best for your solution.
Having said that, SPAs do have some advantages especially if you're targeting both web (HTML) and mobile app solutions since you can build an API and front-end(s) are SPA and native app respectively. They also offer more seamless experience in many cases, but not always since your app becomes heavier.
SEO is an issue. Isomorphic Reactjs is a potential solution, as is server side rendering via phantomjs just for SEO. However, you should also evaluate what parts/content you need SEO on and if your app can be split into server side rendered for SEO content, such as landing page and other free/static content, and SPA for non-SEO content such as post-user-authentication protected content, which will make SEO for SPA a non-issue.