Usually a person is considered a "min" if he believes something that goes against the principles of emunah, even if his mistake was sincere. However, the Rambam writes in Hilchos Mamrim 3:3 that if someone was brought up by minim and was taught their ways from an early age, he does not have the same status as a min. We must talk to them kindly and try to get them to repent and come back to the Torah. Regarding this category of Zionists, we should certainly pray for them to repent.

The same is true for intentional sinners who are not heretics. The Gemora in Berachos 10a says that we do not ask G-d to destroy the sinners, only the sins. "May the sins be gone from the earth, and let them not be wicked anymore." (Tehillim 104:35).

But as for real heretics, we do pray for them to die, as you rightly point out. The question is, why are heretics different from intentional sinners?

The Satmar Rebbe in Al Hageulah V'al Hatemurah Chapter 67 explains this as follows: The Gemara in Avodah Zarah 17a quotes the verse, "All who go to it (i.e. heresy) will not repent, and they will not achieve the paths of life" (Mishlei 2:19). Asks the Gemara: if they will not repent, surely they will not achieve the paths of life, so the second half of the verse is unnecessary! The Gemara answers that it means that even if the heretic does repent, he will die right away. The Maharsha explains that G-d does this out of His great mercy on the repentant heretic. Heresy is hard to resist, and G-d knows that if he were to live, he would be likely to revert back to his old ways. Therefore he causes him to die right after repenting so that he can go straight to the World to Come.

According to this we can understand why we pray for heretics to perish, not to repent. Actually, we are praying for them to repent, but we know that even if they repent they will have to die right away lest they revert back to their old ways.

Of course, it is up to G-d to determine who is a real heretic and who is simply a sinner or an innocent child of sinners.