I think somebody needs to brush up on the three oaths. Of course the frum opposition is to the existence of the State, this is the opinion of the majority of ehrliche yidden. While we are also opposed to the way the chilonim govern and oppress us. Zionism is not just secular government, that is white washing the words of the gedolim Chas v’shalom. There can never be a state run according to the torah without moshiach. Unless you are one of those kahanists, which I highly doubt you are, that is not the frum velt’s main issue with zionism.
As Reb Yoelish famously said, a Yid has to oppose zionism, but if a goy does it is anti semitism. What do you think he meant by zionism? Obviously it was the State’s existence, why would it be anti semitism for a goy to oppose secular values.
Now again you said “Within the Jewish world, the issue is that many Frum people have a problem with a government that is not run according to the Torah and may think that it would have been better for the Jews if such a government had never been founded. ” Notice how that is not different from what I said in the very beginning. Zionism= a “jewish” state, one that we are vehemently opposed to, and daven every day for it to be replaced by melech hamoshiach.
Perhaps, I wonder whether you misunderstood my initial comment and or deliberately tried to obfuscate the issue, but there is no real difference between the olim’s definition of zionism and the goyishe velt’s. If you read over your words, you will see that.