It seems to me that zionists essentially are creating their own religion and turning Yiddishkeit into something that it isn't. I mean would you drink the wine of someone who kept shabbos, kashrus and taharas mishpacha but also did avoda zora? - you wouldn't. So my question is then how does this apply to the zionists. For example, I learn in the Yeshiva near where I live (&&&.) but cannot make it during the week there for mincha because I work during the day so go to &&&.. to daven with a minyan. For chinuch reasons (I have a 3 year old son) I don't enter the place unless I have to as I want my son to know right from wrong, but is it even a valid minyan with regards to the kashrus of the people there? Do we say there is a chezkas kashrus or do we say that your average person there will have warped hashkafos? If they do have warped (zionistic) hashkofos, does that invalidate them for the minyan?
Regards and thanks for spending time regarding my concerns.
On the question of whether a individual Zionist can be counted in a minyan: the Rambam in Teshuva 265 forbids using a Karaite for a minyan, since they do not believe in the concept of minyan. He quotes the Mishnah in Eiruvin 31b, which says that a eiruv cannot be established through someone who does not believe in the concept of eiruv. The implication of the Rambam is that if someone is a heretic yet believes in the concept of minyan, he can be part of the minyan. The Brisker Rav is known to have ruled in accordance with this Rambam. (The Igros Moshe, Orach Chaim 1:23 goes even further and permits the use of any heretic for a minyan. The Satmar Rav in his Teshuvos Divrei Yoel, Orach Chaim 8, disagrees.)
So it would seem that if a Zionist who believes in Hashem and the Torah and believes in the concept of a minyan enters a regular, non-Zionist shul, or a non-aligned or melting pot shul, he may count for the minyan. However, davening in an officially Zionist shul is a different story completely. By entering the building and davening there, you are affirming that their shul represents a valid form of Judaism. It would be better to daven alone than to daven in such a shul.
Now, what is considered an officially Zionist shul? Any shul with an Israeli flag, or any shul that says the prayer for the medinah or the Mi Sheberach for the Israeli army, is an officially Zionist shul. Even though they only say these prayers on Shabbos and you are davening there on a weekday, it makes no difference. This is what their shul represents and you are affirming it as valid.
It is known that the Satmar Rebbe sent his yeshiva bochurim to collect tzedaka in shuls that had a Zionist flag. It could be that this was different because they did not daven there, so they were not affirming it as valid Judaism. They were just entering to find people who might give tzedaka. The Rebbe told them not to answer "amein" or "yehei shmei raba" in such a shul.