I admit to not being an expert on the nuances of Satmar, but this statement put out by one of the Satmar Rebbes (Rebbe Zalman) is surprising to me..

The Rebbe said that it is obvious that one is allowed to go to the draft board in order to get his exemption from the IDF. He also said that the Divrei Yoel (Rav Yoel Teitelbaum) also said the same, and it is too much mesirus nefesh to not go at all and it would be very difficult to say going to the board is prohibited.
source: Haredim10

What is more interesting about this than the little item and understanding about Satmar is the revelation that the Peleg Hayerushalmi people led by Rav Shmuel Auerbach are seemingly being even more extreme than Satmar on this issue