score:2
Generally speaking if you are a citizen of both countries you don't have to receive visa as an Israeli citizen you can receive it as a German citizen for the purpose of visiting Startup Acceleration program.
Secondly even with a B1/B2 visa in your passport your "default stay" doesn't have to granted for 6 months. 6 months is the maximum that it can be granted for by the Border Control officer but they don't have to do it.
Now for the issue at hand.
Which way legal way you choose enter the US makes absolutely no difference to the USCIS as long as you abide by the limitations prescribed by that method. So if you choose to go the VWP/ESTA route you have to abide by the limitations of the program and leave within by the end of the 90 days.
If your schedule will force you to be in the country more then 90 days you should obtain a visa and if you've already used your German Passport to enter the US you might as well continue and obtain a visa using that passport not because using your Israeli passport would be problematic at the US border but because with your German passport you can prove the most important thing that US immigration looks for when granting visas: You leave the country.
Upvote:2
It seems pretty clear that going to Germany for any length of time ends your stay in the US; your subsequent entry in the US would be a separate visit. from the ESTA site (https://help.cbp.gov/app/answers/detail/a_id/1126/kw/esta/session/L3RpbWUvMTQxMDg1MTk3MS9zaWQvUENOeEJ3Mm0%3D):
Your ESTA authorization is generally valid for multiple trips over a period of two years (starting the date that you are approved) or until your passport expires, whichever comes first.
Later:
Receiving ESTA authorization does not mean you may stay in the U.S. for two years. It only allows you to travel to the U.S. under the terms of the Visa Waiver Program (VWP), which only allows you to stay in the U.S. for 90 days or less. If you plan to stay for longer than 90 days, you must obtain a visa at the nearest U.S. Embassy or Consulate.
If you are already planning to go to Germany, you should probably go with option 1: use the German passport.
Note also that if you plan to stay for longer than 90 days (that is, without returning to Germany or going to any other country), you could also apply for the B visa with your German passport rather than your Israeli passport.