In BigCommerce the sales categories are mandatory to create a new item, so that is why Acumatica-BigCommerce connector requires to have at least one category during the export.
I would also recommend you to manage Sales Categories in Acumatica, this will simplify the process and allow you to have one source of truth.
However, if you really need to manage sales categories in BigCommerce only, I can suggest you the following customization that will disable categories synchronization for existing items. Only new items will still require at least one sales category:
Step 1: Go to Item Sales Categories screen (IN204060) and create 1 category with name “Unassigned”. Name can be anything, Unassigned was used just for example.
Step 2: Go to BigCommerce Stores (BC201000) and used Unassigned category as the default Stock and Non Stock Item category. This will allow you to export a new item created in Acumatica to BigCommerce without any error.
Step 3: Publish the attached customization “BCOptionalCategories.zip”. The customization package does one simple thing: removing Sales Categories from the API call if there is an existing BigCommerce item. Because in this case we can rely on the BigCommerce categories.
This will work for even for the first time synchronization if connector has found the BigCommerce item with the same name or the same SKU. Meaning if the duplicate is found, than connector will not override Sales Categories too.
Step 4: Test the solution. Sales Categories will be preserved in BigCommerce.