I am a dual citizen, with a Romanian passport and a Palestinian passport. Can I enter Israel using my Romanian passport?
In principle, there's no problem. As a Romanian citizen you can enter Israel without a visa for up to 3 months.
In practice, security considerations play a dominant role, and provide almost no transparency. You may be denied entry if authorities suspect you of being a risk to Israel, and there are no hard rules saying how they determine this.
Being Palestinian will likely lead to deeper scrutiny. There's no reason for you to present your Palestinian passport, but you shouldn't assume that they won't know of it (I don't know what Israeli security forces know, but they know a lot). You should be able to show that you come as a genuine tourist, and provide evidence for it.
Note that any sort of pro-Palestinian activism, even if you don't see it as anti-Israeli, may lead to denial of entry.
@ugoren answer is basically true - but just adding a bit -
As for the available information to security personnel - On most passports ( actually, to my knowledge - all ) there is a 'place of birth' - regardless of the nationality. if yours states 'Palestinian authority' or any other city name that can be linked to those territories or to Israel - than it would be just like presenting your Palestinian passport .
second - the name and surname reveals a lot - and so does physical appearance.
That being said I am not sure what are the actual law requirements in presenting passports in Israel for a Palestinian passport . I do know that Israelis with multiple passports are required by law to present the Israeli one on entrance and exit - and that is regardless of their other citizenship or residency place. this rule actually applies in many countries so you might want to check on that seeing that the Palestinian authority has its kinks and it is a special entity entity when dealing with the Israeli law. ( For example some Palestinians actually have an Israel issued ID which will also depend on the place of birth or residence )
Another issue is that they may ask you if you posses another passport.In that case you either will be forced to show them the other one ( including stamps and visas ..) or Lie ( not the greatest of ideas in TLV airport ..)