Most browsers battle for the biggest amount of users. In that, such browsers should be able to effectively visit and use any website on the net. This comes with implementation of javascript, cookies and (still) flash.
Makers of these browsers want to gain some money in the race, which leads to implementation of techniques that allow transferring your surfing behaviour to third parties. Some do it openly (Microsoft), some sneaky, some try and get back (Firefox) and some have a user-data-to-cash model as an overall business model (Google). In the mix of open sourcing (parts of) the code, things can be mixed/messed up, leaving the above average user confused (Chromium and derivatives).
A "safe browser" is an ambivalent statement: is it safe in terms of 'not messing up your operating system and/or other software on your machine', or is it 'preventing snooping personal user data to whatever party'. We all hope for both, but our doubts sometimes say we get none.
Most modern and popular browsers have an extensive set of preferences to be set. Some also have hidden features that can be unset with less or lots more effort, if ever revealed at all. Sometimes your settings get (deliberately) changed after an update.
IMHO it is best to have a few browsers at hand, for specific purposes.
lynx,
dillo or
netsurf work safe and fine, but isn't your tool to use this forum or manage your bank account. You can read the morning papers' website on it though. That leaves the 'usual suspects' to participate here, if you like with extensions to monitor or block data snooping: uBlock, Privacy Badger, etc.
The only thing we can do is avoid browsers and their companies with a bad reputation -- on software security, data security or both. Just follow the news to get updates on the Good, the Bad and the Ugly. My personal strategy is also to instantly remove software that misbehaves for whatever reason (freezing at normal use, not upgradable or deletable with
pkg).
Or just switch to safer modes like mail-lists, RSS and IRC.
Just some thoughts...