I’m looking for a Jewish source on an ethical matter. I hope it’s appropriate for this site. Take an action that is on its own permitted and well intentioned, but you know some others will misinterpret you and cause harm. Example, you discuss Israeli politics online and one day you criticized an Israeli policy. It’s predictable that small number of people will misinterpret you and spread hatred of Jews likely contributing to a violent anti-Semitic event. The issue is how much responsibility you bear for another’s actions. Is there a source which discusses something like this which I can read?

Such questions are not only "ethical" but also purely halachic! The Chafetz Chaim writes explicitly that saying something which in unto itself may be fine, but it will lead others to say something degrading, is prohibited as "avak Lashon Harah" (Rambam, Hil. De'ot, 7, 4; Chafetz Chaim, Hil. Lashon Hara, 9, 1-2 and Be'er Mayaim Chaim ibid, 3) How much more so it's prohibited in the example which you gave, where it shows the Jewish people, and accordingly the Jewish God & religion, in a negative light in the eyes of the gentiles, where there is also an issue of the very severe Chilul Hashem- desecrating God's Name (e.g. Yechezkel 36, 20 and on).