Why if my income is under $41,675, I'm paying capital gains tax on my mutual fund holdings?

You pay tax on dividends, earnings, and on sales transactions.   When you inherit stock or other property, your basis is usually the value of the asset on the date of death of the previous owner.  Assuming the asset had appreciated since your mom purchased it, the basis is "stepped up" to current market value, so the income tax on any profit that built up while she was alive is forgiven.  You are responsible only for the tax on appreciation after you inherit the stock.   If the stock price falls before you sell it, you can claim a tax loss.  If the stock had lost value while owned by your mom, your basis is "stepped down" to the date of death value.   From Cost Basis Tracking - Inheritance.  

Your capital gain taxes depend on whether your capital gains transactions are short-term or long-term.   The holding period for inherited stocks is always long-term.   So, if you sold inherited stock, treat it as long-term.   The capital gains rate would be 0% for long-term transactions and taxable income under $41K.   Why do you think you are paying capital gains taxes?  

• Gains you make from selling assets you’ve held for a year or less are called short-term capital gains, and they generally are taxed at the same rate as your ordinary income, anywhere from 10% to 37%.  
• Gains from the sale of assets you’ve held for longer than a year are known as long-term capital gains, and they are typically taxed at lower rates than short-term gains and ordinary income, from 0% to 20%, depending on your taxable income.

The basis of property inherited from a decedent is generally one of the following:

• The fair market value (FMV) of the property on the date of the decedent's death (whether or not the executor of the estate files an estate tax return (Form 706, United States Estate (and Generation-Skipping Transfer) Tax Return)).
• The FMV of the property on the alternate valuation date, but only if the executor of the estate files an estate tax return (Form 706) and elects to use the alternate valuation on that return. See the Instructions for Form 706.

Capital Gains w/ Rates Explained