No, it should not cause an issue with NJ Division of Taxation unless such expense allowed on your federal return is specifically exempted by NJ. For example, New Jersey does not allow federal deductions, such as mortgage interest, employee business expenses, and IRA and Keogh Plan contributions. The assumption here is that the expenses you intend to take on your federal return were incurred in 2021, and once your federal return is completed, then the net profit or loss from your business will be entered on your 2021 NJ return.
There does appear to be two different considerations here, one relating to taxation and one relating to licensure (the ability to legally conduct a business in NJ). While your start-up business expenses, allowed on your federal return, do not appear to be specifically exempted by NJ, whether your ownership and operation of a NJ business prior to license (if that was the case) is another matter for which we cannot offer any advice.
With regard to doing business in NJ and NJ taxes related to doing business, below are two links that you might find helpful.
Starting a Business in New Jersey
NJ Division of Taxation
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