As mentioned before, if the Raspberry Pi 4 is incorrectly identified as an audio adapter accessory, even compliant USB-C chargers will deliver zero volts instead of the 5 volts needed by the single board computer.
Whether your USB-C charger works with the Pi 4 has to do with whether it uses an "e-marked" cable. This non-compliant design breaks functionality with more powerful "e-marked" cables, such as the USB-C chargers that ship with Apple's MacBooks and some Windows 10 laptops.
An e-marked cable uses a chip to make sure that the cable can handle the power or data transmission requirements of the intended use. USB-C issues aren't an unheard-of problem, as the Nintendo Switch also packs a non-standard USB-C port that won't work with all cables, and early phones and laptops equipped with USB-C charging could be fried by rogue cables.
You definitely need a good, stable power supply to power the Raspberry Pi 4.
As an illustration, you should utilize a MacBook Pro charger with loads of USB-C devices.
The Raspberry Pi 4 detects e-marked cables as an audio adapter accessory rather than a charger and refuses to use them to power up the board. The Pi 4 was the Raspberry Pi Foundation's first ever USB-C device, and, well, they screwed it up. The reason boils down to incorrect detection circuitry being present on the Raspberry Pi end of the USB connection. Sadly, in-depth analysis of the board and its design revealed that the Foundation used a more cost-efficient design over compliance with the spec. Upton went on to say, "I expect this will be fixed in a future board revision, but for now users will need to apply one of the suggested workarounds". "It's surprising this didn't show up in our (quite extensive) field testing program".
Check out the new ports: USB-C for power, dual mini-HDMIs for display output. It's actually normative, meaning mandatory, required by the spec in order to call your system a compliant USB-C power sink. It's not a calamity, then - you'll just want to be careful if you're going to use a Pi 4 as the heart of your next DIY project.
If you haven't bought one, you can always wait for the board revision, which should be coming in the "next few months", per Ars Technica.
Fortuitously, it doesn't damage the Raspberry Pi 4, and it doesn't create any fire hazard.