Streetgeek: Can I try answer you without getting stuck in the technicalities of the Zionism Debate? Let’s talk on a general level.
The attitude of “live and let live” is not a Frum attitude. You are correct that you must respect somebody who disagrees with you on the “Chicken V. Shnitzel” debate, or on the “Rosenblatt v. Koussevitzky” issue. Everyone is entitled to his own opinion, and to hate somebody because a preference of his is assur.
“Beliefs”, however, are not a matter of choice. The Torah tells us how to think and act, and our job is to clarify the Torah’s position and act accordingly. And if there are those who act AGAINST the Torah, especially those who are deliberately Anti-Torah, they are evil.
We say every Friday night: “אהבי ה’ שנאו רע. Those who love Hashem despise Wickedness.” This isn’t “שנאת חנם”, this is Sinah with a very positive reason. R’ Meir and Bruria famously disagreed whether to hate the Sin or the Sinners (יתמו חטאים\חוטאים מן הארץ), but both are in agreement that our world is not an egalitarian society where beliefs are a matter of choice. “Acceptance” is the one thing we do not have; we shun and reject falsehood and atheism and anti-Torah beliefs with all of our might.
Seeing people who are not observant should hurt. If somebody would publicly abuse your father, hit him and spit and degrade him, would you be able to just walk past, or would you feel emotionally involved and hurt? Every person who sins is minimizing Kovod Shamayim; is a terrible black stain in the world. It is sad when we sink to the depths that we allow others to sin; that we are so low that we maintain casual indifference to רע. We must do everything we can to promote Kiyum Torah UMizvos, and with that, Kovod Shamayim. And we must do everything we can to protect our sensitivities, that we don’t become numb to Aveiros and Kofrim.
The point of protesting is two fold:
A) “When you are hurt, you cry out”. Regardless of whether or not there is anything constructive to gain by protesting [which there generally is], protesting shows the voice of truth is still fighting. It means not bowing to the Haman by keeping a straight back. Imagine your parents, or you son, was locked up for keeping Shabbos. Would you do everything in your power to release him, and to ensure that others are able to continue keeping Shabbos?
B) It helps us. When you see a Jew doing an Aveirah with casual indifference, it is mashpiah on you. It makes sin more accessible, more real, and less terrible each time. It’s a natural phenomenon. Every time I see a Yid being Moicheh for Kovod Shabbos – shaking his fist at a car driving through the streets, or shouting “SHABBOS!” at the top of his lungs, it guards me from allowing the sight of a casual sinner from ruining my sensitivity to חטא. When hundreds of Yidden march up the roads with all their children, clad in their shabbos finery, singing “Yismechu Bemalchusecha” – it may mean nothing to the Mechallelei Shabbos, but it sure inspires courage, resistance in the Shoimrei Torah.