Same issue is happening on my site. Though, its strange a few anchor links work and a few do not. This like for you all just started a day or two ago. Super frustrating, as my client is about to launch. I want to follow this thread. Hopefully Safari will come out with a fix soon.
www.integrated-awakening.com
The sub heading links that still work are About:FAQ and sometimes About:Contact works. The Services:Pricing does not work on Safari anymore. All anchor links work on Chrome though.