Ugh. I definitely wouldn't want to support Israel with a group that has such misguided racist reasons for supporting Israel. Likewise, I wouldn't want to support Gaza (or, more to the point, oppose the military actions) with the group who is going around urging Israel supporters to withdraw their support.
Is it that hard to disagree with actions of the Israeli government while supporting Israel?
Why is this so hard for some people to wrap their minds around? It's much like how I love the United States, am proud to live here and be a citizen, and spend quite a bit of my time promoting peace and a good quality of life for the inhabitants of the country. I'm also frequently infuriated and embarrassed by actions of our government. Expressing support and love for America does not in any way mean that I agree with our country going around and blowing up brown people (not to mention oppressing our own brown people). Similarly, I love Israel and hope for peace and safety and well-being of the Israeli people, but I really hate that the Israeli government thinks they need to blow brown people up.
What's really frustrating is that so many otherwise intelligent people have this need to make politics so black-and-white. You're either for Israel, or against Israel. I don't feel comfortable going to either type of rally, because I support the state of Israel, but I don't support said state blowing up people. Much like how I support America, but I wouldn't display an American flag (by itself, without other flags or a peace sign or something) on my car or my bag, because it's become equivalent to a pro-war/anti-Arab symbol to so many people. I've heard from a lot of fellow GLBTQ folks who say that when they notice that a business has American flags on its website or displayed on the premises, they become suspicious that the business supports anti-queer causes, and will look further into this before patronizing the business. Upon further inspection, they're often right. The flag has become a warning symbol for many of us.
(Also, I think it's obvious to most people that Miss Kelly is a racist nutjob, but the world isn't as concrete as she makes it out to be. Yes, I support the Ay-rabs who are getting blown up by Israel. I also support the Ay-rabs who are getting blown up by the U.S. It isn't right to blow up anyone. If it makes me a terrorist to not want to see anyone -- Jewish, Arab, Muslim, American -- be a victim of violence, then fine, I'm a terrorist.)
Our synagogue is quite liberal and very much social justice minded. Yet, every week, when we say the mourner's kaddish, we also add "the individuals who have died in the service of this country, and the individuals who have died in defense of the state of Israel." (The wording used by the clergy is always really similar to that; not sure if I've gotten it exactly right.) Sometimes, if there's been a major tragedy somewhere in the world during the week, they will also add those individuals. (I also find it interesting that the traditional kaddish text of course refers to only the Jewish people [ve'al kol Yisrael], but is still used in inclusive congregations where kaddish is said for anyone.) I always personally say the kaddish for the individuals who have died as a result of both conflicts. I wish that we as a congregation would officially include these individuals. I haven't actually spoken with the clergy about doing so (maybe this will encourage me to do so), but I have a feeling that they've surely considered it. I'm purely speculating here, but I have a hunch that including the Iraqis and Palestinians would upset some of the older and more rigid members of the congregation. I can see how the kaddish is something sacred and probably not somewhere to invite controversy, but right now, it's expressing a political view and is condoning oppression, whether people realize this or not.
עוֹשֶֹה שָׁלוֹם בִּמְרוֹמָיו הוּא יַעֲשֶֹה שָׁלוֹם עָלֵינו וְעַל כָּל יִשְֹרָאֵל וְאִמְרוּ אָמֵןּ
Oseh shalom bimromav hu ya-aseh shalom aleinu ve'al kol yisrael ve'imru amen
May the one who makes peace above make peace descend on all. Everywhere.