Why would they block such sites? If your having issues with the site then you should contact the Site WebMaster about the site issues.

But Mozilla is putting a red padlock saying the site is not secure which is often not true. Anyway there should be an easy way for me to overcome this obstruction

Neither the company Mozilla or the Firefox web browser blocks any websites. The web browser is Mozilla Firefox or Firefox for short.

https://support.mozilla.org/en-US/kb/how-do-i-tell-if-my-connection-is-secure https://support.mozilla.org/en-US/kb/what-does-your-connection-is-not-secure-mean