Some themes do that for you, and I have never seen an issue. For example; in the UK, if I search for health insurance, the top result after the ads is
https://www.comparethemarket.com/health-insurance/
white H-tags on a blue background, then blue H-tags on a white background with links in green (not something that I would choose, but they have certainly not been penalized).
Yes, you may be able to say that they have the money to get to the top of the serps regardless of the text color, if I search for "best dog grooming kit for a spaniel" (first LTKW that I thought of that would not give me a huge authority site), you get this:
https://simplyfordogs.com/cocker-spaniel-clippers/cocker-spaniel-clippers/
Their first and last H3 tags are orange, with the rest black.
Go for what you like, if you dont think that you are getting the positions that you like, or you see a fall in ranks after only changing the H-tag colours, change them back (don't forget to come back and prove me wrong though!).