I was getting constant Direct X crashes, so I did some searching and found that XIV apparently doesn't cooperate with high clock speeds on graphics cards. I lowered my clock speed by a little bit and haven't had one since. FFXIV was the only game I've had this problem with.

For reference, I've got a GTX 1080ti, and generally use ASUS GPUTweak II. The Overclock and Gaming Modes give me crashes in XIV, if I switch the the Silent Mode (which lowers clock speed), no crashes.