Israel Security is a "nightmare" as you have described it , only if you turn it into one in your head .
The reason they are asking you to login to you computer, is only to assure that it is yours and that you are not transporting someone's else computer ( one of the questions they ask you is if everything you carry is yours ..).
Another reason is to see that the computer is functional and it is not a masked device ...
In my visits to Israel on business I was asked to turn on or login to many devices , from cameras to HD to electrical drillers to welders.... Nothing to do with your social profiles.
After YOU ( not they ) log into the computer , that is it . they themselves will not touch your computer . They are not allowed to . Nor do they want.
Can you refuse ? YES.
Is it a good Idea ? Probably not .
That will only raise suspicions and will make further problems .
Regarding social networks - No one can even know if you are registered to any specific social network or not . No one will ask you to login to any account from any other computer . These stories simply can not be accurate .
on a side note I will say that Israel is one of the most advanced high tech nation in the world , if not THE most advanced . If they really want , believe me they will have no trouble getting into your phone without asking your permission to do so. They did it to the nuclear facilities in Iran. you really think your phone is more secure ( or more interesting ) than that ?
Further more - I bet that half ( if not more ) of the components and software in your phone and computer are directly or indirectly connected or developed in Israel - without you even knowing it. :-) from intel chips to google products.
They only ask these things to see your reaction and attitude.
It is called "profiling".
... AND - Israel is not the only country to do that - I was asked to login to my computer in at least 10 different countries - and in one ( China ) I was not even asked to. they just took the computer and did what they wanted themselves .
So, to answer your direct questions :
Can you refuse ? - Yes you can refuse ( also legally refuse ) and ask for a lawyer or a court order .
I was body searched in Israel and I was asked to sign a waiver form.
You can refuse to sign. Wait for a court order. Lose your flight.
The consequences ? - You will get an honorary place at a not-so-nice list of some sort .
Is it worth it ? I guess not .
Best practice ? If you really are afraid - Ask an Israeli colleague to accompany you. they will ask him some security questions about you - Easiest way to cruise the security there.
Last remark - those occurrences happen on your Departure . Not arrival.
By then - your attitude towards Israel ( and their security procedures ) would probably change and you will have absolutely no trouble.
If it will not change - So try to fake it to change .
Like others have wrote here - Sometimes it is better to be smart than right .
EDIT / UPDATE :
like I wrote in some of the comments , it is strange that this question is targeted to Israel only . I think that it is a valid question, but maybe it should be addressed to other ( all ?? ) countries as well, for example - the US.
US immigration might soon ask for travelers social media accounts
Official U.S. Federal registry
Although not yet implemented - this demonstrate the currents and winds in the airport security industry , and weather we like it or not - also the direction where it will eventually might end up.