Search engines, often viewed as reliable gateways to information, tailor search results using customization algorithms based on user preferences, location, and more. While this can be useful for routine queries, it raises concerns when the topics are sensitive or contentious, possibly limiting exposure to diverse viewpoints and increasing polarization. To examine the extent of this tailoring, we focused on the Israel-Palestine conflict and developed a privacy-protecting tool to audit the behavior of three search engines: DuckDuckGo, Google and Yahoo. Our study focused on two main questions: (1) How do search results for the same query about the conflict vary among different users? and (2) Are these results influenced by the user's location and browsing history? Our findings revealed significant customization based on location and browsing preferences, unlike previous studies that found only mild personalization for general topics. Moreover, queries related to the conflict were more customized than unrelated queries, and the results were not neutral concerning the conflict's portrayal.