I'm not sure I entirely agree with some of these points. For example I don't think
@psychotick's friends arm bending trick is completely relevant. The reason for the discomfort is, I think, not because the backwards bending is alien per se but rather because both you and she are human and you know that your body, and most other people's bodies, can't do this without this without breaking. However you don't feel any of that kind of discomfort when looking at say Octopuses (octopusi?) or snakes which are far more 'alien' to us in their movements.
Some may have atavistic reactions to some body forms. So for example if the alien is insect like in its appearance then there are some who will go to pieces just because of that. Or arachnoid the same. But I think it's unlikely all or even most would react like that.
On Earth life has occupied pretty much every niche available and we have environments ranging from ice to super high temperatures in which life manages to survive and over the millions of years life has been around it's tried just about every viable configuration with varying degrees of success. Throughout all of those iterations the solutions have certain commonality. Only looking at higher lifeforms that have at least some chance of achieving technological intelligence those will include some form of motile ability (legs, flippers, wings), ability to manipulate your environment (arms, hands, tentacles, trunks, prehensile tails), ability to reason (brain or some equivalent). I can't imagine anything much more outrageous being successful in an alien environment that has not been tried somewhere sometime on Earth.
Early on there were some pretty wacky life variants but they have always been superseded by more efficient alternatives, a process still going on today. And nothing that life has produce in the last 100 million years or so has been so outrageous that it would cause the sort of complete abandoning of reason as has been speculated on. Terror, maybe, if coming face to face with the likes of T-Rex.
Also it's not too difficult to understand pretty much all of these life variations. I don't mean down to the ability to communicate directly (we're not doing so well with any of our native life on that front) but rather understanding their motivations. All motile life that has ever been on this planet is driven by pretty much the same motivations: survival of the gene, escape the predator and hunt the prey. I see no reason to believe any life from anywhere in the universe would be driven by any significantly different motivations and therefore produce any significantly different structures.
So personally I believe we would probably be able to understand them on a basic level but whether we could manage to communicate is another matter (I refer you again to our ability to communicate with the like of Dolphins for example). I believe that if we ever find life out there we will find whole ecologies of parallel evolutions rather that incomprehensibly alien ones. One of the great failing I see sometimes in SF creations of weird aliens is any plausible progressive evolutionary road to get to that point. The best attempts at this that I have see probably come from Neal Asher, in particular in his Spatterjay books. But even there, though extreme, the weird alien lifeforms are still comprehensible and still obey those fundamental motivations.
So I don't think the hypothetical aliens will be too surprising in form or too incomprehensible in motivation.