My website is on a shared host platform. For over five years I was able to send smtp email via gmail from server side script but it stopped working a few months ago and Google support says it is most likely because gmail now requires sha-256(https://productforums.google.com/forum/#!topic/gmail/wmG4idip8nM). But is this the responsibility of my web host provider? My web host provider has no idea what I am talking about and says it has nothing to do with them. sorry if I came to the wrong place to ask.
Your website does not require a SSL certificate, what Google is referring to is sending emails over SSL. To do this you must use TLS/SSL to send the email, what this means is that your sending emails over a secure connection.
It sounds like your script it outdated or it requires some changes to the settings. Gmail and other emails providers send mail using port
25 but for a secure (TLS or SSL) connection this is port
465. Depending on the script that you use it could be as simple as changing the port number from
465. If further help adapting the PHP code then your need to ask on Stack Overflow.
In the event that you are connecting over a secure connection then its likely your web host will need to update their OpenSSL version. This is easy and almost instant. Any good web hosting company should be doing stuff like this already.
The whole panic of Google abandoning support for SHA1 was that many secure websites used SHA1 certifications. So, since your website doesn't require SSL, there is little to worry about.
However, since your website has a contact form it would be a good idea to get a SHA2 SSL cert installed on your hosting. Google will reward you some SEO benefit for it too, how much is anyone's guess.