@hakatan
Regarding the Chareidim in the Zionist parliament, that is halachically almost-impossible (read Rav Reuven Grozovsky’s biayos haZman). And according to the Satmar Rav and others, it’s severely prohibited.
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It is more than ‘possible’…..
Haredim in Israeli Parliament is not only possible , but accepted halachic practice dating back to the very first Parliament in 1949.
This is supported by the overwhelming majority of Poskim ,Rabanim and Rashei Yeshivot in EY and in in Huts La’arets, not only as ‘permitted’, but as a Chov Gamur and as a Mitsva.
Some Kana’im do not participate , but this has no bearing on accepted halachic practice , as mentioned.