Yes. You should continue to carryover and claim your capital loss. The standard deduction is separate from your capital loss and has no bearing. Your capital loss reduces your income prior to applying the standard deduction. If you do not use your $3,000 in capital loss carryovers, your taxable income will be $3,000 higher for the year.
While you may already have $0 in taxable income, there may be instances in the future where the capital loss is valuable. For instance, capital loss carryovers can be used to offset future capital gains and are not limited to the $3,000. If you have gains in the future, they can be offset by any remaining loss. Unfortunately, the only way to have the losses available for use are to use the available $3,000 against ordinary income and track the carryover losses on your tax return each year.
@gmhigbee
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