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airsail said..
Uli Boards have patented the Wiki rail, it tries to address the lack of a sharp rail on an inflatable.
Note that a sharp rail has less grip, but more planing speed: the water can escape the rail without drag. Water will try to wrap around round rails on exits, which creates drag... but also provides hold. In a nutshell, the sharp "wiki" rail is for speed (hence the name), not grip, and thus is aimed at sailboading an inflatable.
For SleepLessInTLV: Inflatables can definitively surf, it will make you go through the basic learning stages: learning how to move on the spot, taking off, bottom turning, and following the wave. This should amount to a fair nu,ber of sessions. Afterwards, you can get a rigid board for learning rollers and more advanced surfing. And at this stage you will be more confident to avoid hurting people.
So learning to surf with an inflatable SUP (or surf) is actually a good idea. Try to get a not too thick one (4" / 100mm is OK), and a modern (more rigid) one. Check that it has a good front rocker (nose turned up). Be careful, some brands are really more heavy than others, and a lighter board is more enjoyable.