Note that secular Israelis, who appear to be the economic and political elite, i.e., the ruling and/or upper class, are NOT complaining about government institutions coercing their children into becoming frum. They are making no demands for “secular” accommodation. They are not complaining about over-representation of religious Jews in the officer corps of the military. The fact that they dominate the country is strong evidence of the bigotry towards the non-elite groups (the religious, and especially Hareidim and religious non-Ashkenazim).
It has been well documented that the secular-run army has the effect of moving a considerable percentage of Jewish recruits into a secular lifestyle they did not have previously, and that it appears that the biggest determinant of whether a young Israeli brought up religious does, or does not, “go off the derekh”, is military service. One should note that this takes place before they run into the significant discrimination in employment they encounter after the military.