WordPress Site login problem with facebook, twitter and other social media

You, and those plugins, should be using the HTTP API to make connections. That API will attempt to make a connection in several different ways. If your site is capable of making HTTP requests that API should be able to do it. That is largely the point of the API:

The problem is that web hosting servers support different transports
and some might support none. The solution then is to support as many
as possible to allow for those who have hosts that disable one or two
to still access the web through one of the other transports that might
still be enabled or supported.

If the HTTP API can’t make a connection you will need to convince your host to alter their server configuration, or (much) more likely change hosts.