The good news: multiple H1's are no longer anything to worry about, and haven't been in a while. More good news: if it still bothers you, you can modify your WordPress theme.
Headings are used to provide structure on a page. Your single blog post page, for example, should probably only have one H1, because what else would you use as a blog post name tag? On the other hand, your Category page may display multiple blog post titles, descriptions, first paragraphs, etc. All of these blog titles might be H1's.
Search engines' reliance on headings has decreased since HTML5 introduced new content structure, with
section tags. Having multiple pieces of standalone content on a page is commonplace. Search engines know this. This is why, if your page has an H2 instead of an H1, the lower level heading will be treated by them as an H1. Just make sure the heading copy is relevant to both humans and search engines.
That said, if your website theme was coded in a way that doesn't make sense semantically, you may want to just make changes or create your own hierarchy. In that case, make a child theme, and working in your child theme go into the PHP templates for your various content pieces and make the necessary changes. You may also need to update how your various headings look in the style.css file. If all of that seems too much, you may need to change your theme, but this might result in a number of other website issues.