View based on months or days - display certain items during specified times of the year
Here's an idea for something you could do in the Drupal admin UI (using only modules that are part of Drupal 8 core) since it seems you don't have access to the codebase.
As you noted, the date field requires a year.  So you can't use it if you want your months to be year-agnostic.
I assume that your requirement is &quot;each node should be assigned to one or more months&quot; and we don't have to worry about days (for example, a node could be &quot;January and February&quot;, but it could not be &quot;Jan 12 - Feb 10&quot;).
In that case, you can add a field of type List (Text) to the node content type that you want to sort in Views.  For the value of the field, enter the 12 months and allow multiple values so that multiple months can be selected.
Then, you can configure the view to filter based on your month field.  To set the current month, I'm pretty sure you can use Twig date in a Views filter to input the current month (not tested, from memory).