State-to-state 1031 - Do I need file non-resident state tax?

Yes, you do.  Your sale is subject to a withholding tax of 3% of the sales price if the price is over $20,000.

Per Georgia 1031 exchange rules:

• Withholding: 3% of the sales price if the property is over $20,000.
• Exemption: Individual or entity that owns replacement property desired by the taxpayer.  Sellers performing a 1031 exchange and acquiring replacement property in Georgia are exempt and must submit Form IT-AFF3. Nonresident sellers purchasing replacement property out of Georgia are not exempt.
• Further Information

Many thanks, Alicia. This is very helpful.

The link for Further Information is somehow timed-out.

I found the document below on the GA DOR website. Doesn't this mean the like-kind exchange is exempted?

Q. Is withholding required on a like-kind exchange of property?
A. Withholding is not required to the extent the income from the sale is not subject to Georgia income
tax.

https://dor.georgia.gov/information-georgias-withholding-requirements-sales-or-transfers-real-property-nonresidents

Your link from 2011 is a bit outdated; however,  form  IT AFF3 is proof that you are safe and not taxed. See IT-AFF3 Seller's Certificate of Exemption.

@ZMint