Having good keywords and links from other sites is likely a bigger impact on your SEO than using React, whether or not you're using SSR. Performance can reduce page ranking, but we should also (then) be asking, "Do <Framework X> Web Apps Have Poor SEO?"
Server side rendering and testing pages through fetch-as-google to make sure they’re being picked up by bots. It’s not as big of a problem as people make it out to be. There are plenty of fixes but this combination is simple and effective.