When using my phone to search for information.........I find a site that looks useful and click on it.....only to find, many times, a banner saying I have to consent to their use of cookies.
Sometimes I think "ok, I will accept" but in most cases I dont want companies I have never heard off checking on me.
Is it possible to by-pass this and still get on the site ?
In most cases, yes. How you disable cookies depends upon which browser you're using, but disabling all cookies will break most sites. e.g. if you disable all cookies you'll no longer be able to be "logged in" to any site or add anything to a cart or anything dynamic like that. And a lot of sites will straight up refuse to work without cookies.
However: In Chrome's privacy settings there's one that says "allow third-party cookies" which will block most of the trash if you turn it off and will be less damaging to your experience than blocking everything.
As of this year Firefox has tracking protection built-in.
Can't speak for Safari but Apple have always put a big emphasis on their privacy stuff.
Despite being a major PITA, the popup is a good thing because it's informing people about how insidious the online ad market is when there are literally thousands of companies listed under these things. Though I suspect most treat it just like an End User License Agreement and just scroll past without reading
