Thanks Rectro! I found it: https://forums.cgsociety.org/t/restrict-simulation-to-2-axis/1690057/6
Unfortunately, the described method is only for objects not points if I understand Srek correctly (Srek's example scene is no longer online).
Yes, I guess the only way is xpresso and iterate though all points to restrice the Y axis, hmm.... I still don't understand why connectors are not working.