I try to login with OpenID (stackexchange.com provider) with third-party cookies disabled and NoScript (with sane setup: always allow main domain).
First you need to click two times "temporary allow all" to be able to click on the Stack Overflow login-button. Then you shortly see the login page, then you get redirected to a page "you do not allow third-party cookies, click here". After clicking, there finally is a working login form.
This is a lot more hassle, than you would expect from a professional site.
Login without third-party cookies should work. If this needs an intermediate step because of OpenID, there should just be a button "take me to the no-third-party-cookies login" instead of showing the login page and then redirecting to a page with only a link, which eventually points to the real login page.