I have done it, never my first choice, NEVER WITH SMALL WORK PIECES EXCEPT WITH A JIG WITH SECURE HOLD DOWNS, always with a jig longer than the work riding on a bearing and or a starting pin or curved starting surface, and for god's sake NEVER ON A SHAPER.

The best way to insure shallow cuts is with a bearing kit that limits the depth of cut, using decreasing size of bearings in 1/16" increments.

As I said first, climbing is never my first choice, but on some curved work on a router it may be the only choice short of tear out on at least part of the work piece. And for some narrow work pieces a freehand router has not enough bearing surface to work. Building a jig takes less time than reattaching a finger.

Oh, safe? No, I never really feel safe climb cutting. Its a game of minimizing risk and exposure.