As religious Zionists usually go to a Shul that says the prayers for Medinat Yisrael and Tzahal, i would have thought that the worshippers would want to show their identification by standing fort hose prayers. However I find more and more, that many with knitted kipot do not in fact stand, some do only for Tzahal. I would imagine that for ideological reasons, that it should be a MUST to stand. Even if one can argue that the State does not always do things in accordance with the Torah, and the government may do controversial acts (Oslo agreement, disengagement from Gaza), the prayer for the states does not bless the government as a prize for their activities, but blesses them to act wisely and in accordance with the Torah, and later on blesses the people living in Eretz Yisrael, so what is wrong with that. Also, we ask Hashem to look after our soldiers defending our borders, we don’t ask for anything else. So what is the problem? If we don’t do this, how can we come to the Chareidim and complain about their lack of recognition of the State and army?
Shalom U'verachah, There is no real halachic requirement to stand for all the prayers and only for certain ones. This does not reflect on the importance of these prayers, for example, we sit for reading the Shema even though this is one of the only prayers that is a Torah obligation. Usually standing up is a sign of respect for a prayer and if this is the custom of the entire community then it should be followed. But the most important thing is to show respect for the prayers and what they stand for, whether one stands or sits. Kol Tuv