Well I ended up with my phone being checked
Upon learning that the Israeli security wasn't that troublesome, I booked two mileage runs to TLV. One same day return ATH-TLV-ATH on A3. And two days later, ATH-FRA-MUC-TLV-MUC-FRA-ATH on LH with 3 nights in Israel. The things one does for 560QP and 820P with Miles&More

My plan for dealing with security at TLV was to be totally honest and cooperating with them and trust their judgement.
After landing in TLV, I walked with the crowd to the passport control. A couple of guys stood in the walkway, they let everyone else pass but pointed at me: security! No idea if they disliked my face or were specifically looking for me due to my booking details. They took my passport, asked about the purpose of my trip. I honestly told that the only reason for the trip was to earn 260 frequent flyer points and that I would be flying back to Athens in the evening. Oh, and I would be coming back to Israel in two days for 560 more points!
We talked about frequent flyer points, about the countries I had been to and people I knew there, about my job and my income. I showed them my bookings and my mileage account. At one point they gave me my passport back and I was free to go.
Next came a passport control booth with a curious lady inside. "Purpose of your trip? Name of your grandfather? Do you know anyone in Israel? Do you know anyone apart from your classmate you want to visit? Do you know anyone apart from your classmate and people from FlyerTalk? I don't understand why you are in Israel! Where is your luggage? Why is your luggage in Athens? Why Athens at all? You knew you were likely getting questioned here but you still came here?" In the end, she told me to sit in the corner of the passport control hall and wait for my passport.
While waiting, I heard an Israeli security guy tell someone else with graphical details what would happen to them if a search of their luggage revealed a smartphone they supposedly didn't have with them.
Finally, an older bald guy waved me in: interview! I sat down across a desk from him in a separate room. He asked the same questions, also asked about my private life. Upon hearing that I chatted with my classmate in Israel on WhatsApp, he wrote down his number (but never called). He then asked if he could see my WhatsApp. I agreed but asked him not to message anyone from my account. He appeared dismayed at the suggestion and told me he did no such things and his only concern was his country. I was kind of relieved he asked about WhatsApp, because it is not too private and clearly shows hat I am very pro-Israel and why, starting with my school friends being mostly Jews.
He browsed my WhatsApp for what felt like 5 minutes, the smartphone remained in my sight but I didn't see what he was looking at. He clearly found something of interest, because a few times, he stopped scrolling and read carefully. Then he told me my short stay duration is what triggered a red flag and I was free to go. The border crossing took 1h20 in total.
I rode a train into the city and explored the city with an electric scooter for 3 hours, stopping for a coffee at the beach, then went back to the airport. There was a desk where travelers are asked questions before proceeding to check in/security.
"Purpose of your trip?" "To collect 260 frequent flyer points!" "Please stand aside!" The lady at the counter phoned someone.
A likeable Jewish guy in a suit in his early 30s came and introduced himself as a security supervisor. He was very friendly and told me he knew people sometimes fly just for miles and that it was not a problem at all. We talked about my travels and he asked me about my trip to Dubai (meaning he had access to what I said during the entry interview). Then he laughed and asked me why I was so nervous. I didn't feel that nervous and told him so, but he kept repeating the question. Finally I confided to him that I was indeed slightly nervous, because if they classified me as a security threat, I could be forced to check in all my hand luggage.
He stepped aside and talked to a female colleague for a minute or so. She then came over, introduced herself as a supervisor and repeated exactly the same questions. She then talked to him, he phoned someone, and then I got a red sticker with a barcode on my passport, my barcode scanning app showed the barcode started with a "2". I guess it's a good score for a non-Jew. No more hassles that day.
Two days later, I again landed in TLV. On the walk to passport control, I noticed the same guy who stopped me 2 days ago. He recognized me: "are you back?" -"as promised!" - "welcome back!" At the passport control booth, the lady working there only asked me about the purpose of my trip ("tourism, visiting a classmate and earning frequent flyer points") and whether it was my first visit, then she read something on her computer screen and I was good to go. Border crossing duration: 2 minutes.
I spent 3 amazing days in Tel Aviv and Jerusalem, then it was time to depart. A lady at the security counter asked me about the purpose of my trip and if my luggage had been with me all the time. I admitted the luggage had been sitting in a hotel luggage room for 2 hours and got the feared yellow sticker with a number starting with a "6" and some handwritten note. I mentioned that it wasn't a good idea to leave the luggage at the hotel, but the lady smiled and told me it was not a problem at all, I just needed to go to a special counter to have it scanned.
I walked to that counter, my luggage went through a CT scanner. Then they removed the yellow barcode, leaving a red barcode starting with a "2" and I was good to go. No further hassles.
It was a very interesting border experience, with security people who actually had brains and border people who were more interested in the person than in the person's documents. I would have no concerns about going to Israel again, even on a same day return MR. But YMMV...
Tourism wise, I visited Tel Aviv and Jerusalem (the old town and Yad Vashem). Loved it, except for food prices - twice as expensive as Germany! Since I also had a MR to Jordan the week before, I visited the Dead Sea from the Jordanian side. Indeed, with most of Jordan being freezing cold, down there at the Dead Sea the air temparature at daytime was like +20C and the water felt like +24C, so I did get to swim!
Thanks to everyone who replied in this thread!