btw, I went to the israeli embassy in NYC to renounce. they will do every thing to stop you from doing so. claiming you are missing a document, that you had a kid, that your marriage licence isnt signed properly. I tried 4-5 times already. At this point im ready for an (anti) Israeli immigration lawyer if someone has recs.
I was there a couple of weeks ago. They wanted me to first register my kids as Israeli, so I had to get them birth certificates with Apostille. After submitting everything they asked "do you have proof of birth? (הוכחה לפרי בטן). We looked at them as if they came from a different planet, and said "what do you mean, we just gave you certified birth certificates?" The response was "we need hospital discharge papers". Our immediate response to them was that they are out of their minds, there's nothing else we will give them, and if they don't want to accept what we gave them we will stop the entire process. We don't want to register our kids as Israeli, they are making us do so. After a few minutes they came back and said everything is OK.
They accepted all the paperwork, and told us that they will complete the process in our absence. A few days later I got a call from them asking me to come and sign paperwork to make my kids Israeli. I said to them that we had just done all of that, to which they responded that we need to sign the papers that they prepared in our absence. When I asked if they need both myself and my wife to come or just myself, I was put on hold and then was later told that they will email me the documents to sign and return. The documents were emailed (terrible quality scan), I printed signed and returned. I am now waiting for them to call me for the next step.
The person taking our documents also said that the chances of the renouncement being approved are low, but based on my research that is a bunch of BS. One needs to put a reason on the application for renouncement. From what I managed to gather, as long as there's clear evidence that the person's permanent residence (for a while - the longer the better) is outside of Israel, and a valid reason is given (not wanting to have the hassle of traveling with two passports when I go to Israel should in and of itself be a valid reason, add to that not wanting to pay VAT on car rentals, not wanting to subject myself and/or kids to military service, etc.), and as long as there are no outstanding military or financial obligations, it is likely to be approved.