I am currently filing both my husband and my taxes - married filing separately. I am trying to change both of our deductions to standard, but the system won't allow it.

You can switch between the standard deduction and itemized deductions by following the detained instructions in the TurboTax article  How do I change from the standard deduction to itemized (or vice-versa)?

Also go to My Info and Edit your name  or your spouse's name  and continue, there is a question ...Either spouse or I claim itemized deductions.  It should be  unchecked.   And just checking, you are using 2 Online accounts, one for each of you?