Compatibility issue? I've been shooting a mirrorless (Sony A6300) underwater for the past ~5 years, and I haven't found it yet
That said, both mirrorless and SLR cameras have their pros and cons. Early mirrorless cameras used contrast-detection autofocus, which lagged significantly in speed behind SLRs' dedicated phase-detection array. As time went on, most mirrorless cameras gained on-sensor phase detection autofocus, and eventually surpassed SLRs in both features (eye-detect AF is now common on mirrorless, but cannot be implemented on SLRs) and speed, albeit the latter is only true for the highest-end models, primarily Sony A1.
There are some points in either direction when it comes to lens selection, especially underwater. The only mirrorless platform with native fisheye lenses is micro four thirds, with both Olympus and Panasonic offering an 8mm fisheye option. However, most mirrorless systems can use SLR fisheye lenses via adapters, Canon 8-15mm being the most popular choice on full frame and Tokina 10-17mm on APS-C. On the other hand, mirrorless systems (with the exception of Canon RF and Nikon Z FX) have native lenses that are compatible with wet optics, which is not the case with SLRs, and while it's possible to adapt SLR lenses to mirrorless, it doesn't work the other way around.
A significant advantage of EVFs/screens, as opposed to OVFs (optical viewfinders) are the focusing aids that are available - you have magnification, focus peaking, zebra striping, after-shot review, etc. A weakness, however, is shooting into the sun - when you have sun in the frame, it's just this giant ball taking half your field of view, so framing becomes mostly guesswork, whereas with OVFs it's much easier.
If you're shooting video, then by necessity any camera that you use is mirrorless - even if you're using a DSLR, the mirrors are locked in the open optical path position, turning the camera into a mirrorless equivalent.