I am entering my W-2 and I was a FICA exempt employee (Student working at the school I go to). Social Security and Medicare were not withheld from my paycheck. However when I enter in my W-2 it reduces my Federal and State refund by half. My wife has a regular job and taxes were withheld as normal. Is there something special I have to do so we don't get dinged by this?
No.
This is how tax works. Your W-2 earnings are taxable, and if there is not enough withholding taxes, your tax refund is reduced.
That seems odd given that the wages in question are exempt. Why would they count towards taxable income for those categories?
The wages are exempt for Social Security and Medicare taxes, Not for federal income taxes.
Wages paid for certain student work are exempt from FICA taxes but are taxable for income tax.
Please read this IRS document for more information.