The Rabbanut courts have expressed their independence frequently, especially when rejecting conversions performed by Orthodox rabbis abroad. They rejected these conversions, and upheld the rejections, even when the Chief Rabbis vouched for the converting rabbi and said his converts should be accepted.
Ivanka Trump was the most famous of the cases rejected by the Rabbanut. Actually, they never rejected Ivanka Trump's conversion, but they did rejected the conversion of someone else converted by the same rabbi (Rabbi Haskel Lookstein), so it has been assumed that the Rabbanut would reject the conversion of Ivanka Trump as well.
With Ivanka Trump now being the First Daughter, and expected to be very influential in the White House, if not hold an actual position in the upcoming government, it makes me wonder whether the Rabbanut will change its tune or not.
The other situation is that of Jenna Jameson. Jenna Jameson has been going through the conversion process, Orthodox, for a while now. Just the other day she posted online as to finally having completed her Orthodox conversion. I have no idea what rabbinical court led by what rabbi performed the conversion, but I do wonder if the Rabbanut would accept it or not, should she decide to make aliyah with her Israeli husband.
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