Safari is widely considered a pretty safe browser and if there's a list of companies concerned about our privacy out there Apple is near or at the top of it. I'm not sure why "privacytools.io" doesn't talk about Safari, but I have very little trust in sources that I've never heard of.
I believe that privacytools.io may be more concerned about whether the browser company - Apple, Microsoft, Google, or Mozilla - would be able to deliver browser history, stored favorites, etc., if they receive a legal warrant for that information. Apple syncs some of this data with iCloud, Google has their own sync, Im not sure about Microsoft, and Mozilla also can sync this data. Of course you can choose not to sync the data, but Apple would definitely be able to gather and deliver this information in response to a warrant.
Another concern is the ability to use "fingerprinting" of the browser to prevent tracking and following you even without using cookies. It's talked about right on that page. Firefox can be configured using tools to help prevent tracking, following instructions on that page. See this link on their page; test it in Safari, Firefox and Chrome if you wish:
https://panopticlick.eff.org
You may not have heard about privacytools.io, but I have. Here is a transcript of an episode of the Security Now podcast from a couple of years ago, when I first heard about it:
https://www.grc.com/sn/sn-514.htm
BTW, I think that stuff is pretty propeller-head and unnecessary for most of us. However, if you are a journalist working in a country without free press protections, for example, the recommendations on that page may be critical to you. Otherwise, it's nice to know.
I believe that Safari is reasonably secure, but it is not patched as often as Firefox or Chrome. Then again, almost every exploit I read about, such as at the recent Pwn2Own competition, require somebody to have access to your computer in order to exploit the device through the browser. If you think that people can break into your computer, you may want to follow those recommendations more closely.
I know that Chrome sandboxes each browser tab, I believe that Firefox is starting to, and Safari sandboxes plugins to help protect your computer from being exploited from web sites that you visit. Sandboxing will definitely help keep you more secure.
Another guess about why privacytools will not recommend Safari is because Safari has few third party extensions to add security, and doesn't have the rich configuration tool like Firefox's "about:config" page to change default options to allow greater security.
I use Safari myself, because I use an iPhone and an iPad and it allows me to quickly handoff from those devices to my Mac. I trust that it is reasonably secure for the way that I use it. I have used Chrome and Firefox in the past, but Safari I think uses less battery on the Mac, is pretty fast, and has those other advantages, so that's what I use.