How to solve the issue with the design after switching to html5?

Question

css

What's the problem - I removed the wordpress markup to make everything html5, as google swears at it.
But after removing the rel="category tag" code, it turned into title=Rock, which completely negates my edit of the category button of different colors for different categories of such a plan .category-rock .cat a {color:red;}.
How to implement with the current template the individual design of the category buttons so that they display a different color everywhere (main, single, tag page, and so on), and not just on the category page, since the old code still works with a bang.
Now this is the structure. What code should be written in CSS to set custom design options for each category button?