THAT is interesting in itself. Shinui isn't an anti-Orthodox party
Then why do most of their pronouncements
solely attack Orthodox Judaism and Orthodox parties (for those here who don't know Israel there are political parties to represent pretty much every small interest group- from about a dozen religious parties, to Arab interests, to secular interests, to outright Communists, Anarchists,etc).
As for the dropping state sponsored Orthodox schools that is especially telling. For those who don't know the education system in Israel there are a few truly private schools (but not many). The state provides funds for about a dozen school systems, from National Religious (Zionist and Orthodox), to purely secular, to basically Communist, to Arab, to "Black Hat" (Yeshivish and Chassidic) Orthodox. Many of these systems, like large systems everywhere, are corrupt. Yet the only one they attack are the Orthodox schools. Incidentally most of the religious schools do indeed teach math (all of the National Religious schools teach secular studies, and the Haredi teach the minimum the state requires). With all the dozens of school systems, and abuses in most, Shinui is
only calling for cutting off Orthodox schools, yet somehow they aren't anti-Orthodox???
On other subjects, Orthodox and National Orthodox Jews are different.
The latter join the Army, found settlements, and support the RKBA (a rare thing here).
The former dodge the draft
Please do try to be more honest.
Some Orthodox in Israel (most Haredi) do not get drafted. Full-time study in Yeshiva is one of about a dozen catagories that provides a draft excemption. Most Orthodox men, in Israel and in the US, spend many years in Yeshiva (it is not so they don't have to serve, it is because we believe in learning and serving G-d). Honestly taking a deferrment that is there is not really "dodging".
Additionally many Orthodox do indeed serve. The National Religious are Orthodox. Last numbers I saw are that about 30% of the total officer corps is National Religious while 50+% of the junior officers (those under 30) are National Religious (Orthodox). Additionally, many serve as enlisted soldiers, and they disproportionally serve in combat units. Also, before you change your attack to "only" the Haredi let me point out the unit in Nahal (an infantry unit BTW) that is a Haredi unit, an entire unit made up of Haredi, and a handful have always served in National Religious units (I personally know a few Haredi who have served in National Religious units). Heck, there is even a very popular set-up where people can split their time between Yeshiva and their unit in the Army.
We are as likely as non-religious Jews to own guns and support gun ownership (most of the Orthodox Jews I know from Israel own guns), and settlements (while I won't get into if they are a good or bad thing) are not a religious only thing (there are plenty of secular settlements).
They have also distributed leaflets promoting death penalty...
Here I won't comment on whether it exists or not since I've never seen it and it is pretty much impossible to prove something's non-existance. However, I will point out a few things about the death penalty in Jewish law, something either you don't know, or you are being intentionally misleading since outside Jewish practices the "death penalty" has a very different meaning.
First, there are many things under Jewish Law (Halacha) that deserve the death penalty (including breaking the sabbath). We do not go around killing sabbath breakers (and never really have). What it means is that certain behavior
deserves the death penalty. However, G-d, not us, administers it. If you do something requiring the death penalty you may well die prematurely (when born we all have a set number of years, an experation date so to speak, and if we do too many sins, especially certain kinds, we may die earlier). Also, when there is a human administered death penalty (there hasn't been in thousands of years) it is very strict. There must be 2 witnesses who warn the transgressor that they see the action and that it is a death penalty offense. Even so a beis din is very hesitant to institute the death penalty to the degree that a beis din (Jewish court) that puts someone to death more than once every seventy years is blood thirsty.
So, even if true, the meaning is very different from what you are implying here.