It is unlikely that free WordPress themes will hurt your SEO because themes and search engine optimization are two different things. However, if a theme is not designed to be SEO friendly, it can cause some type of harm to your site.
WordPress themes have a reputation for being SEO friendly and this applies to both free and paid or premium themes. They come with proper responsive and are bereft of hacking code and nulled code. Theme coding or view is not the issue. It can affect the speed at which the page is loaded which in turn can affect user experience and hence the SEO of your website.