I was sent a 1099-NEC for am the cost of a membership I need to do my job. How can I report this as an expense?

Since you cannot do your job without the access to this membership, this is indeed considered compensation and is correctly reported on the 1099-NEC.  You, however, also have the expense of the membership in order to perform your services. 

You need to report the 1099-NEC as self-employed income and the same amount as a Subscription Expense for the business.