Magento 2: Apache mod version not enabled/installed/allowed by host, causes 500 error on all pages due to failing .htaccess files

This problem is caused when apache's mod_version module is not enabled. Unfortunately, my host does not allow me to enable this module and so I have devised the following workaround:

Step 1

Open [magento_root]/.htaccess with your favourite text editor.

You will notice, towards the end of the file, there are numerous entries following this format:

<Files composer.json>
    <IfVersion < 2.4>
        order allow,deny
        deny from all
    </IfVersion>
    <IfVersion >= 2.4>
        Require all denied
    </IfVersion>
</Files>
<Files composer.lock>
    <IfVersion < 2.4>
        order allow,deny
        deny from all
    </IfVersion>
    <IfVersion >= 2.4>
        Require all denied
    </IfVersion>
</Files>
...

Step 2

The exact procedure here is dependent on the version of apache that your server is running. Mine runs 2.4, so I have removed all <IfVersion /> statements and replaced them with the content of their relevant clause, like so:

<Files composer.json>
    Require all denied
</Files>
<Files composer.lock>
    Require all denied
</Files>
...

This process must be repeated until there are no instances of <IfVersion /> remaining in the document.

Step 3

Open [magento_root]/pub/.htaccess with your favourite text editor and repeat the process laid out in step 2.

Note: In the event that this process has been carried out and then the apache version is changed (i.e. the server was running apache 2.2 and upgraded to 2.4), then files must be restored by replacing both edited files with the relevant .htaccess.sample, and following the above process from the beginning.

As mentioned in Erica Southworth's answer, the list I provide is not exhaustive, but it is all that is needed in order to recover basic functionality. Here is the list of all files containing IfVersion queries, for continuity:

app/.htaccess 
bin/.htaccess 
generated/.htaccess 
lib/.htaccess 
phpserver/.htaccess 
pub/.htaccess 
var/.htaccess 
vendor/.htaccess  
setup/config/.htaccess 
setup/performance-toolkit/.htaccess 
setup/src/.htaccess 
setup/view/.htaccess  
vendor/magento/magento2-base/.htaccess  
pub/media/customer/.htaccess 
pub/media/downloadable/.htaccess 
pub/media/import/.htaccess 
pub/media/theme_customization/.htaccess  
vendor/magento/magento2-base/vendor/.htaccess 
vendor/magento/magento2-base/var/.htaccess 
vendor/magento/magento2-base/pub/.htaccess 
vendor/magento/magento2-base/phpserver/.htaccess 
vendor/magento/magento2-base/lib/.htaccess 
vendor/magento/magento2-base/generated/.htaccess  
vendor/magento/magento2-base/dev/.htaccess 
vendor/magento/magento2-base/bin/.htaccess 
vendor/magento/magento2-base/app/.htaccess  
vendor/magento/magento2-base/setup/config/.htaccess 
vendor/magento/magento2-base/setup/performance-toolkit/.htaccess 
vendor/magento/magento2-base/setup/src/.htaccess 
vendor/magento/magento2-base/setup/view/.htaccess  
vendor/magento/magento2-base/pub/media/customer/.htaccess 
vendor/magento/magento2-base/pub/media/downloadable/.htaccess 
vendor/magento/magento2-base/pub/media/import/.htaccess 
vendor/magento/magento2-base/pub/media/theme_customization/.htaccess

Note you will need to remove the "IfVersion" commands from every .htaccess file in Magento, after the installation too. These are the files I had to modify with a fresh install Magento2 (2.4) and on the godaddy linux platform.

app/.htaccess 
bin/.htaccess 
generated/.htaccess 
lib/.htaccess 
phpserver/.htaccess 
pub/.htaccess 
var/.htaccess 
vendor/.htaccess  
setup/config/.htaccess 
setup/performance-toolkit/.htaccess 
setup/src/.htaccess 
setup/view/.htaccess  
vendor/magento/magento2-base/.htaccess  
pub/media/customer/.htaccess 
pub/media/downloadable/.htaccess 
pub/media/import/.htaccess 
pub/media/theme_customization/.htaccess  
vendor/magento/magento2-base/vendor/.htaccess 
vendor/magento/magento2-base/var/.htaccess 
vendor/magento/magento2-base/pub/.htaccess 
vendor/magento/magento2-base/phpserver/.htaccess 
vendor/magento/magento2-base/lib/.htaccess 
vendor/magento/magento2-base/generated/.htaccess  
vendor/magento/magento2-base/dev/.htaccess 
vendor/magento/magento2-base/bin/.htaccess 
vendor/magento/magento2-base/app/.htaccess  
vendor/magento/magento2-base/setup/config/.htaccess 
vendor/magento/magento2-base/setup/performance-toolkit/.htaccess 
vendor/magento/magento2-base/setup/src/.htaccess 
vendor/magento/magento2-base/setup/view/.htaccess  
vendor/magento/magento2-base/pub/media/customer/.htaccess 
vendor/magento/magento2-base/pub/media/downloadable/.htaccess 
vendor/magento/magento2-base/pub/media/import/.htaccess 
vendor/magento/magento2-base/pub/media/theme_customization/.htaccess