You can tell that the prohibition on Gaza is a rule on the post-processing. Bing does this too sometimes, almost giving you an answer before cutting itself off and removing it suddenly. Modern AI is not your friend, it is an authoritarian's wet dream. All an act, with zero soul.
By the way, if you think those responses are dystopian, try asking it whether Gaza exists, and then whether Israel exists.
To be fair, I tested this question on Copilot (evolution of the Bing AI solution) and it gave me an answer. If I search for "those just my little ladybugs", however, it chokes as you describe.
Not all LLMs are the same. It's largely Google being lazy with it. Google's Gemini, had it not been censored, would have naturally alluded to the topic being controversial. Google opted for the laziest solution, post-processing censorship of certain topics, becoming corporately dystopian for it.
Wait... It says it wants to give context and ask follow up questions to help you think critically etc etc etc, but how the hell is just searching Google going to do that when it itself pointed out the bias and misinformation that you'll find doing that?