Guide for: "Ideally I'd like to not have a Google account at all but want to keep up to date with the few Youtube channels I follow."
Download an RSS extension for your browser. I chose one called 'RSS Feed Reader', it doesn't matter which one you choose but I may change because this one wants to charge me after the trial expires. It shows a number at the top telling me how many new videos there are.
A videos feed for Youtube is one of the following:
And here's how to find those:
Put those puppies in there, name them the name of the channels you are following. Now whenever a new video is uploaded to one of those channels they show up in your RSS and you don't need a damn Google account or to be logged in or even need to be on the website. Your browser will just check for you.
The extension I'm using lists the titles of the videos I haven't seen, and clicking them opens the video in a tab.
For anyone reading this in the future I'm now using Zebra RSS and it's a lot better than the previous suggestion. It basically gives me a video list with thumbnails and without the trial bs. It's free.