For the donuts to be invisible, you need to make sure that the smallest spatial frequency in your image (i.e. detail) for an out-of-focus area is larger than the bokeh-size for that out-of-focus region.

In other words, if you have point-lights (e.g. light glittering off rippled water, streetlights, fairylights, etc), then you will get unavoidable donuts. If the background is all fairly uniform in tone and has no fine features (points or lines) with strongly separated tones, then it will all tend to blend together despite the donut bokeh.

If you're shooting birds against the sky, you get no issues. If you shoot birds in front of shrubbery, the shrubbery can look bad because all the lines get doubled.