If you are regularly clearing cookies on close then it doesn't make much difference either way. Cookies only become a problem when they persist over time.

Extensions can block cookie banners and auto-decline cookies. Does it still happen in Troubleshoot Mode?

Yes. I had to sign in again after a restart in troubleshoot mode. Then I deleted all cookies, website data and cache, and washingtonpost.com still did not ask to accept cookies. However, when I wanted to answer your question, I had to sign in again in my Mozilla account. Any further thoughts on possible hidden cookies WashingtonPost.com finds in Firefox that it doesn't in Opera?

Try disabling Tracking Protection for the site and disabling your extensions.

Also try disabling DNT and GPC.

There were no extensions enabled. Tracking Protection and GPC were already disabled.

Enhanced Tracking Protection ETP was enabled, now disabled. After disabling ETP via the shield icon at the left of the address bar, WashingtonPost.com asked to accept cookies.

Thank you so much, zeroknight. You gave great advice" I appreciate it very much.

Well, now I wonder whether it would be better to read the WashingtonPost with ETP enabled. Any thoughts?

See also Block cookie banners on Firefox.