From experience 2 years ago, I'd say this is perfectly safe if you take the same basic precautions as you'd take anywhere else in the world. It's the most 'African' of the whole East coast route. (Link to blog below). It's the part of Africa to take your time in.
Things since then have changed in Egypt, but read this ride report from Biking Marco.
He seemed to have an equally good time as us in Egypt, extending his visa to 2 months as we did.
There were demonstrations in Khartoum for a while recently but things seem fine now. My daughter's there at the moment arranging to ship her bike back to UK. (She worked there until recently but got a promotion to a job in Kigali). My son-in-law still lives there and is loving it.
Ethiopia is often cited as the most 'difficult' country. Here's my take on that.
We were brilliantly advised by a couple travelling north by Land Rover, that we met in Sudan.
The best bit of advice they gave us, that we adapted for motorbike travel, was that they always kept their windows open so that they could instantly engage with local people, most importantly by getting their arms out of the windows quickly to wave and shake hands.
Shaking hands is fundamentally important in N.E. Africa especially between men (including with policemen and border officials).
Outside of Addis Abeba, visit Ethiopian traditional-live-music bars - you'll get a great welcome and the music is brilliant.
(As in all countries, take normal care in the big cities, the towns are usually much safer).
Have a great trip.