I didn't hear clearly which Western websites cannot be accessed in China. I have no experience using these websites, and I don't know if they are blocked or not. But I believe its possible that some websites may not be accessible.
SIIO Director Lu Wei, on October 30, 2014, in response to this question from an Asahi TV reporter: “Facebook and other Western websites are inaccessible in China, why has China shut down these websites?”i
Facebook has long been blocked in China and Instagram has not been available on major android markets in the mainland since July.
Global Times, September 30, 2014, “Instagram Blocked”ii
Net users in the Chinese mainland are experiencing one of the longest and strictest blocks on Google and associated websites, with analysts predicting that it may continue amid tensions between the US and China over cyber security.
Global Times, June 17, 2014, “Google Block Set to Continue”iii
Chinese authorities say they have blocked messaging apps KakaoTalk and Line as part of efforts to fight terrorism, South Korea said on Thursday, the first official explanation of service disruptions in China that began a month ago.
Global Times, August 8, 2014, “Govt Tells S.Korea it Blocked KakaoTalk, Line, Other Apps to Help Fight Terrorism”iv
In recent years, more and more Chinese Net users are forced to seek alternatives to surf the Internet outside of the Great Firewall (GFW), China's Internet infrastructure, by using mirror websites that show blocked Google search results, or by using VPNs.
With the blocks on Google showing no signs of being relaxed, analysts are predicting that the market for VPN services - which range in price but with most of the easily available options selling for around 98 yuan ($15.7) each month - is going to expand significantly.
Global Times, July 13, 2014, “Use of VPNs Skyrockets as Legal Quagmire Remains”v
[S]ince Facebook and YouTube have been blocked by China's firewall, improving their relationship with the Chinese government may not be easy.
China Daily, October 2, 2014, “Facebook, YouTube Refuse to Delete Terror Material”vi
Surprised to find that Google had become accessible around midday Monday, Chinese mainlanders posted the news online, which went viral on social media immediately. A jubilant group of Net users assumed that it was because of some kind of agreement between the Chinese government and Google. However, later that evening, the website was blocked again, with many people speculating that the temporary access resulted from an update to the Great Firewall. . . .
It might not be worth figuring out what really happened.
Global Times, December 16, 2014, “Open Internet Not at Odds with Regulation.”vii
Many Net users in the Chinese mainland discovered Saturday that they could not access their Gmail accounts, even through third-party services.
Global Times, December 30, 2014, “Gmail Completely Inaccessible Inside Chinese Mainland”viii
Since both Google and China haven't given an explanation and meanwhile Gmail is a technically complex system, there may be some puzzling reasons behind the incident.
If the China side indeed blocked Gmail, the decision must have been prompted by newly emerged security reasons. If that is the case, Gmail users need to accept the reality of Gmail being suspended in China. . . . We only need to have faith that China has its own logic in terms of Internet policy and it is made and runs in accordance with the country's fundamental interests.
Global Times, December 30, 2014, “Gmail Glitch Fuels Unnecessary Speculation”ix
vi http://usa.chinadaily.com.cn/china/2014-10/02/content_18692058.htm (subsequently deleted)