How and when can websites overcome VPN?

[unicorn]

We are traveling in Europe, and using VPN set for Los Angeles. Yet sometimes some websites we use recognize that we're in Europe, and have left us a note blocking us, including the Los Angeles Times and WOW Presents (which hosts RuPaul's Drag Race). Even when we're signed up in the same city, I notice that some days those website let us have access, and sometimes they don't. Do some websites have the ability to "see through" VPN, and is there a way to get around that?

[Moses]

Log out from site and clean cookies when logged to VPN and flush cache of browser. Use proper private VPN (many public VPN are in the "Black list"), check "Do not track" in browser settings and "do not allow third parties cookies", then log in again.