Yes, you can still take the deduction.
MO follows the federal itemized deductions unless stated otherwise. The deduction for personal property taxes on vehicles as a federal deduction that is not included in the items subtracted.
Here is the language from the MO Tax Instructions:
MISSOURI ITEMIZED DEDUCTIONS Missouri law requires a taxpayer to start with the federal itemized deductions reported on Schedule A of his or her federal return. If a taxpayer itemizes deductions on their federal return, they may itemize deductions for Missouri or take the standard deduction, whichever is to their advantage. If the taxpayer does not itemize his or her deductions on the federal return, they will not be allowed to itemize on the Missouri return. If the taxpayer is required to itemize on the federal return, they must itemize on the Missouri return.
ADDITIONS TO FEDERAL ITEMIZED DEDUCTIONS Social Security Tax, Medicare Tax from W-2’s and Federal Form 8959, Railroad Retirement Tax (Tier I and Tier II), Self-employment Tax claimed on Federal Form 1040, Line 57 minus Line 27, and Federal Form 1040NR, Line 55 minus Line 27.
SUBTRACTIONS FROM FEDERAL ITEMIZED DEDUCTIONS
The amount of state and local income tax claimed on the Federal Schedule A,
less any city earnings tax included in that amount. If Federal AGI is more than
$313,800 for Married Filing Combined or Qualifying Widow(er); $287,650 Head
of Household; $261,500 for Single or Claimed as a Dependent; $156,900 for
Married Filing Separate, consult the worksheet on Form MO-A, Part 2.