My trackpad recently ran out of batteries and rather than replacing them I decided to see if I could get by without it. It is an interesting experiment.
One issue I ran into is that on your login page the buttons for logging in with Google and Facebook do not have a tabindex associated with them and use html span tags so there is no way to click the "Log in using Google" button on this page using only your keyboard.
There is no way someone who is not a developer would know to do that though.
I think it probably makes more sense to make these html
<a> tags and then the browser should take this into account automatically.
That should improve this page's accessibility.