Refund not Taxable but showing up as taxable on Turbo tax

You should be enter each individually even if they were both received in 2023. 

By entering them each, the program will ask for each year. 

In your situation, since you used the Standard Deduction each year, enter zero as the Taxable Amount for each refund.

I did that.  It didn't ask for the one from 2021.  Once I hit continue, it just takes me back to the first screen and when I check my 1040 it's listed as taxable income.

Delete the one from 2021 and then re-enter it.  It should allow you to enter $0 when you re-enter it. 

Still didn't ask.  And it is still being counted as taxable income.

I suggest you delete both 1099-G forms and not enter enter them as they are not taxable if they are refunds for tax years for which you took the Standard Deduction.

I can't see your return, but perhaps the program is picking up one of the 1099-G as Unemployment or something else. 

To Delete a Form  using TurboTax Online:

Select Tax Tools on the left side-bar

Select Tools from that drop-down

Select “Delete a form” on the TOOLS CENTER screen

Select the form, schedule and/or worksheet you wish to remove, in your case both form 1099-G

They are both for state tax refunds, not for unemployment.  Both the Illinois and Wisconsin ones for 2022 are working, just not the one for 2021 and it's in the same window.  Plus, it has it on the St Refund Sheet as taxable.    

Turbo Tax should fix this as I see the same problem reported in prior years. 
https://ttlc.intuit.com/community/tax-credits-deductions/discussion/re-is-1099-g-taxable-or-not-seeing-both-depending-on-tax-year/01/2648223/highlight/true

Instead we are told to not report it because it's not taxable anyway?

I don't have that version of Turbo Tax.   I have Intuit Turbotax Premier and NOT the online version.  There is only one 1099-G tax form on the left margin, and that is one for unemployment, and that's legitimate.  The other ones don't even show up, though I went into the form for the St Refund Wks and changed that taxable amount to $0.  We shouldn't have to change anything inside the forms on TurboTax but I see no other way to do this.

I have the Premier Windows version, not the Business version.  I don't have that screen that you reference.

If neither 1099-G is taxable in 2023, then you can simply not enter them in TurboTax. 

Of course, this means that the IRS has gotten copies of tax forms (the two 1099-Gs) that you did not include on tour return. This means that it is possible that the IRS will notice this and send you a letter. Therefore, you should be prepared to respond that a limitation in the tax software necessitated that you not enter these forms, since that was the only way you could get the proper result on your return. This will not shock the IRS.

So the result is (1) a correct return, and (2) you are prepared to explain what you did to get it if any one ever asks.

Given that many 1099-Gs are not taxable, the IRS may or may not even notice.

I have a similar issue.  I received a refund for 2021 in 2023 and received a 1099.  I itemized in 2021 but I did not get the benefit of all of the state income taxes that I paid in 2021 because of the SALT limitation of $10,000 for deducting state income taxes.  There is a place at the bottom of the State and Local Income Tax Refund Worksheet for state refunds from 2021 or prior years.  If I enter the refund for 2021 received in 2023 Turbotax wants to tax it.  There should be a place where one can calculate how much of a refund for 2021 or earlier is taxable; but, there is not. 

For years earlier than last year, you have to calculate the taxable portion yourself by reviewing Schedule A.

The tax software does not import those years.

@tkent1234