Being denied entry to Israel due to political activism?

German citizens (born in 1928 or later) do not require a visa to enter Israel, so there won't be any background check in advance.

As to the background check at the border, I'm not sure where you're getting your information from about this: "Realistically the Israelis will do a digital background check ... natural language processing of everything you wrote on Facebook included". I have been to Israel many times and know numerous people who have been as well, and have never heard of any such thing. It seems like an urban legend, I'd be very curious to see the source.

If you think about it, there is no reliable way to match you to a Facebook profile - your name might be spelled differently on Facebook from the passport spelling, there may be many people on Facebook who share your name, etc... Matching a person to one or more online profiles is a big research project, and certainly not something that a border agent will waste time doing for everyone who comes in, especially from a European country. I am pretty sure they will just check your name against known crime databases and such and simply stamp you in, I've never heard of anyone being questioned about their political beliefs upon entry to Israel.

Also, Israel does have freedom of speech, with even some Israelis openly expressing pro-Palestinial views. It's not a totalitarian country by any means. I seriously doubt that you can legally be denied entry due to your political beliefs. Also, I've met Europeans (Germans included) in Israeli hostels who were openly pro-Palestinian, who have visited the Palestinian territories and then made it through Israeli checkpoints without any issues.

A few additional points:

• Of course, if you're so actively involved in anti-Israeli activities that your name has specifically made it to watchlists, you're in bigger trouble of course. But simply posting your opinions online and donating to a cause, especially to a legitimate registered organization in Israel like the one you linked to, is not nearly enough to get any serious attention. If you're buying or selling munitions or something, you may have a bigger problem :)
• You may be confusing airline security screenings with entry into the country. During an airline screening for a typical Israeli flight, they can and will ask you about anything at all, from your family to your political views, but that's to determine if you're a threat to the flight, not to decide whether or not to let you into the country. If you cooperate, the worst that can happen there is usually a more thorough search of your luggage and more security measures for you (e.g. can't move around airport secure zone without an escort).
• Even if for some reason you do face tough questions when entering the country, remember that even the toughest questions and the "tense atmosphere" are there not to question your beliefs, but to see how you respond under pressure. There are unfortunately many individuals who would do much more to hurt Israel than just post on forums; If a border guards are asking tough questions, it's only because they want to determine as quickly as possible whether you pose any real problem, and the best way to do this may be to apply some pressure. But if you're not a real threat, as long as you cooperate they will see this, and nobody will waste any more time on you; Again - there are enough real threats to deal with.
• Note that all of the above is based on my personal experience with Israel (I actually hold an Israeli citizenship as well) and the experience of my circle of friends, relatives and acquaintances, and some common-sense / knowledge about the country that I've built up. I don't have any access to the border guards' manuals, so there's always the chance I'm wrong :)

It is a recurring subject in the Norwegian press that Norwegians are regularly refused entry to Israel without obvious reasons.

This problem is also addressed in the travel advices on Israel from the Norwegian Ministry of Foreign Affairs. They write that if you can be assumed to be a moslem or of Arab origin or if you have participated in political or missionary activism, you may be subject to a thorough interrogation and background checks. Failing to fulfill the requirements for the interrogation and/or background check may lead to a refused entry. It is known, that passengers are refused entry without further explanation. If you are denied entry, you must be expected to be held in custody under poor conditions until it is possible to return to your origin country.

It is of course impossible to even guess if you will or will not have problems entering Israel. Considering that the previous text is written in a diplomatic language by an official ministry, you probably however have a good reason to assume that Israeli immigration may reject you if it can be easily determined that you have participated in internet discussions and expressed an "incorrect" opinion.

I have heard of entry refusals of American citizens who had announced in advance online that they intended to enter the Gaza Strip (at a time this was physically feasible). But something like half the American Jewish community is disappointed with Israeli policy. It would be a very big blacklist.

Many of my friends here in Israel support organisations like Breaking the Silence. This is not unusual. Of course, being citizens we cannot be refused entry and we generally whiz through passport check without any hinderance.

I suspect being active in the BDS circles might earn you thorough questioning, but who knows? Much like any border police, the Israeli authorities don't share their profiling rules, but if you just cooperate and you're not up for anything too subversive, you'll be out of the airport in no time.

For a personal edge, some of my friends and Couchsurfing guests shared stories with me. Here's the most extreme one:

A young Swiss citizen, whose father was born in the West Bank. Traveling with his girlfriend, Though his family has long moved to Switzerland, where he was born, the passport control stopped him for questioning. In the meanwhile, his girlfriend was permitted entry instantly, as would be expected for a holder of a Swiss passport, and had to wait for him. Finally, the officer pulled up his father's ID and photo on the computer screen (yeah, modern governments scare me too), and upon confirming his identity, permitted his entrance.

The whole experience was obviously unpleasant and distressing to my guests, but I think overall they've enjoyed their trip.

If you're interested in more horror stories, you can find some here (note, this is an Israeli publication -- we do openly discuss such issues around here). Take it with a grain of salt; journalism is naturally sensationalistic. ("Man bitten by a dog" is not news, "Dog bitten by a man" is.) I'm sure you've heard about people being questioned by the US border police as well, yet it doesn't deter most people from travelling to the US.

It's best to be smart about it. There's no need to discuss your West Bank travel plans with the officer, especially if your plans include something as mundane as visiting churches in Bethlehem and snapping photos of the wall. Do not joke about bombs, do not get into political arguments, apply the same common sense as with any other border police officer around the world.