When you decide on a WordPress theme to use for your website, SEO may not be one of your concerns, but there are a few ways in which the theme can interfere with your SEO efforts:
- it can obstruct search engines from fully index your content if links in it were not created with SEO in mind
- it can create a messy site structure with badly rewritten URLs; search engines may not be able to figure it out easily and will miss your important content
- it can create multiple URLs for the same page that will lead to a duplicate content problem; search engines will randomly split ranks between all indexed URLs, and as a result your your pages will stay buried in search results
Google will not penalize you for any of the above. But those issues could still make your pages less visible and more difficult for customers to find.
To figure out if the theme is problematic, run your site through a service that simulates what a search engine would see, for example https://smallseotools.com/spider-simulator/ or https://theseotools.net/spider-simulator. If all intended text and all links from the page are showing in the result, then the theme is ok.
Another danger of an unknown theme is a messy site structure. To check if this is an issue, use the “Coverage” report in Google Search Console (Google Search Console >> Index >> Coverage). It will show errors, warnings, and other details about the index status of your website.
Once you chose a SEO-friendly WordPress theme, keep your website in a good shape with a SEO plugin that helps to prepare content for thorough indexing and spot potential issues. All in One SEO Pack and WordPress SEO by Yoast are both good choices and are both free. Their premium versions have more features and offer even more help.