Why does Turbotax say the standard deduction is zero?

And that is only one of the limitations  to filing separately -

If you file MFS (Married Filing Separately) keep in mind that there are several limitations to MFS.  Married filing Jointly is usually the better way to file.
 
A few of those limitations are: (see IRS Pub 17 for the full list

<a rel="nofollow" target="_blank" href="https://www.irs.gov/pub/irs-pdf/p17.pdf">https://www.irs.gov/pub/irs-pdf/p17.pdf</a> page 21

1. Your tax rate generally is higher than on a joint return.
2. Your exemption amount for figuring the alternative minimum tax is half that allowed on a joint return.
3. You cannot take the credit for child and dependent care expenses in most cases, and the amount you can exclude from income under an employer's dependent care assistance you are legally separated or living apart from your spouse, you may be able to file a separate return and still take the credit. For more information about these expenses, the credit, and the exclusion, see chapter 32.
4. You cannot take the earned income credit.
5. You cannot take the exclusion or credit for adoption expenses in most cases.
6. You cannot take the education credits (the American opportunity credit and lifetime learning credit) or the deduction for student loan interest.
7. You cannot exclude any interest income from qualified U.S. savings bonds you used for higher education expenses.
8. If you lived with your spouse at any time during the tax year:
   a. You cannot claim the credit for the elderly or the disabled, and
   b. You must include in income a greater percentage (up to 85%) of any social security or equivalent railroad retirement benefits you received.
9. The following credits and deductions are reduced at income levels half those for a joint return:
   a. The child tax credit,
   b. The retirement savings contributions credit,
10. Your capital loss deduction limit is $1,500 (instead of $3,000 on a joint return).
11. If your spouse itemizes deductions, you cannot claim the standard deduction. If you can claim the standard deduction, your basic standard deduction is half the amount allowed on a joint return.

- If you live in a community property state you must allocate community income between both spouses..
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- Community property states.   If you live in Arizona, California, Idaho, Louisiana, Nevada, New Mexico, Texas, Washington, or Wisconsin and file separately, your income may be considered separate income or community income for income tax purposes. See Publication 555. <a rel="nofollow" target="_blank" href="http://www.irs.gov/publications/p555/index.html">http://www.irs.gov/publications/p555/index.html</a>

 
See this TurboTax article for help with this.
<a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/questions/1894449-married-filing-jointly-vs-married-filing-separately">https://ttlc.intuit.com/questions/1894449-married-filing-jointly-vs-married-filing-separately</a>

<a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/questions/1901162-married-filing-separately-in-community-property-states">https://ttlc.intuit.com/questions/1901162-married-filing-separately-in-community-property-states</a>