What is Infringement?
How Can Someone Sue Me if I'm Not Making Money Off My Work?
Anyone can argue any thing in court. So the question becomes whether or not the law backs them up. In this case, if you use someone else's musical composition or sound recording you need a license. If you haven't obtained a license, even if what you're doing is for free or even a charity, then they can sue you. The only exception to this is Fair Use, which is more limited than most people think.
What Damages Can They Claim?
Put yourself in the shoes of a songwriter or musical artist and imagine some situations. If someone sampled your hit single and gave away my remix for free, could you lose out on possible sales/streams? What might happen if someone recorded an acoustic version of your song and it went viral instead of yours? Even though they didn't make any money, they've affected your sales and market value with their version.
Let's imagine a even little more worse. If someone took your song and started playing it at a political rally while they walk on stage, or used it in a video supporting a social agenda you're against. Would you feel well represented? Would your personal brand be unaffected?
These are all questions to consider when dealing with copyright infringement. The courts examine the purpose and character of your use, the impact on market value, and how much copyrighted material is used when determining damages or if it falls under Fair Use. It may not always be intentional and you may not make any profit from it, but if the damage is done you will be liable for it.
copyright.gov - Copyright Basics
copyright.gov - Definitions
copyright.gov - Fair Use Index
publiccounsel.org - Copyright & Fair Use Basics for Nonprofits
smallbusiness.chron.com - For Profit Vs. Not for Profit Copyright Laws & Fair Use Issues
mondaq.com - Ten Key Copyright Issues And Pitfalls Every Nonprofit Should Know