you don’t necessarily need acceptance by hard lefties, although that is not impossible, but if it would be good if you aim to get acceptance/respect from other pro-religious and traditional people in the “middle” of political spectrum. If you can form a position acceptable to such groups (and maybe do some compromises with them, not simply hope that they’ll join all your positions) – then you can have 60% support instead of 51% and with that, you’ll find a way to change political system.
This method is easier to see in US – here people are forced to be in 1 of 2 parties. So, each of them tries to one hand find consensus within itself and at the same time broaden the coalition. When the majority has 51% support – there is always some chamber that is not under control, or one senator who decided to switch, it is not working. When one side achieves a larger consensus that it is able to change character of the country for decades to come (including assigning judges). It is harder to see in Israel as groups continue coalition bargaining even after elections, and people tend to form narrow political groups, but it should work the same – elect a larger coalition and then you’ll change what you want. For example, the things you don’t like in Israeli system are often a product of pre-1970s system when left had a super-majority.