Thanks for trying but it is still telling me to - "sign in to confirm your're not a bot"
Kurt
This sounds like an IP block of sorts; Google has decided that the IP address, or addresses similar to it, which your request is coming from exhibits behavior they don't believe is legitimate. Often, this is through no fault of your own, but rather someone who has a similar IP address, or a matching ISP identifier (ASN). And most sites take the approach of just letting you do a "captcha". VPN users often run into weird security hiccups like this, since VPNs mess with the location metadata, and the authentication provider could see this as suspicious ("George was just in Delaware 5 minutes ago, and now they're signing in from Brazil, this doesn't seem right, gonna ask George to verify")
I don't know what to suggest here, other than maybe try using google.com to do a few searches, and then see if you can click youtube links without being forced to sign in. There are also third-party sites meant to get around this, but then those sites become privy to knowing what videos you watch through them, and they have their own ads which may or may not be as well curated as Google's advertisement service.
These videos should not require a sign-in, and most other providers just ask you to do a captcha if the connection seems suspicious, so I'm a little concerned too that you may have a malicious browser plugin/extension hijacking google sign-in links to get you to give them your PW. You can check if the webpage asking you to sign in is legit or not, by verifying that the address does actually contain "google.com" in it, and that there is a familiar lock icon next to it. For extra peace of mind, you can click the lock, look at the details of the secured connection, and see the actual certificate the website is presenting to prove its authenticity. You'll see a "Common Name" field which should be familiar and not weird (like, google.com, and not g00g1e.com).
You can try this with GRF too, where we can see that we get our certificate "signed" by google. So, when your browser trusts Google's certificate authority, it will trust certificates that were signed by them too. ("You know I'm google, and I know this is GRF. So, you can trust that this is GRF because you trust me and I signed off on it")
It's also worth just reviewing your browser extensions. Look for a jigsaw puzzle piece icon, and there should be an option to manage your plugins, such that you can remove any ones which look suspicious, if any exist.