Should I not update the plugin?

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There are several points which should be clear when starting such a project.

  • WordPress is constantly updating, think about extra layer protection
    through updates or changes in the GUI. (meaning by that, updating
    core files)
  • A plugin relies on WordPress core, which need to be updated also when
    there are changes which can cause conflicts. In worse case it holds
    the plugin from working if not to block WordPress completely from
    working caused by code which caused a major conflict.
  • Never ever change corefiles from either WordPress itself or a Plugin.
    The reasons are obvious and speaking for itself.
  • You can/should write own code when changes are needed for WordPress or
    a plugin. Create a plugin or add it to functions.php in the theme.
    There are often options to ask a developer if it is possible to help
    you with problems and the community can also help you out.

The website doesn’t need to be secure.

The only information being stored is names and some personal information.

Ehm sorry but, names and some personal information, no need to be secure?

  • What about students who are eager enough to invest time to see how secure the school systems are and what more.
  • What about the connection with the Internet (if one exist), no need to secure because nothing will/can happen?

Maybe you think again when mentioning such en public in a society anno 2016 and you want/need clients for living. (yes sorry maybe synical/harsh but hey, that is how I think about such)

So in the bottom line, the answer for the question as it:
Should I not update the plugin

You should always update a plugin when changes are important enough to keep all running as wished.
Yes, sometimes you can skip an update if the changes are not major enough (for the plugin itself or WordPress) in personal cases.
But hey the ‘only’ thing that can happen when not updating is that a client will start complaining because WordPress and/or plugins are not working as expected, in worse case it does nothing anymore.

This is just my personal opinion and maybe others have a totally other view and agree with your way of handling it.

Cheers.