It's doubtful that TurboTax would ever treat a code Q distribution as taxable. Check Form 1040 (or 1040-SR) line 4b. It's only being treated as taxable if it's being included there.
Note that If you would otherwise be eligible for a Retirement Savings Contributions Credit, a Roth IRA distribution could reduce or eliminate that credit, making it appear as though the distribution is being taxed when it is instead causing a loss of this tax credit.
My data entry shows the total distribution from1099-R at 4a on the 1040, zero at 4 b on the 1040and Q at column 7 on the 1099-R. All of my contributions were by 2005. No early withdrawals. What questions in TurboTax could be tripping me up?
What is it that would cause TurboTax to ignore my data entry of zero at 4b?
What you describe is correct and you are not being taxed on the distribution. Line 4a shows the distribution amount, it does not mean that it is being taxed. The code Q is causing TurboTax to properly exclude the entire amount from the taxable amount on line 4b.
With a code Q distribution, no matter how you respond to the follow-up questions the distribution will not show up on line 4b as taxable income.