Even if you take away the "personalized search" component of a search engine like google, the search results are still ranked by some kind of search algorithm. In google's case, that algorithm is based on social network analysis, which basically means it's a popularity contest of a sort, and it also takes into account things like your location. You could obscure that with a proxy, but that still doesn't eliminate the fact that there is an algorithm that's trying to rank your search results based on your query and a lot of data it has from around the web. So you may eliminate some of your search-history-related biases and replacing that by selecting sources that are based on something like a population average, but it won't eliminate general media bias, biased language used in your query, or stories that have already gone viral, and obviously it won't stop you from still selecting the websites you think contain "good" information. When you type in your query, the adjectives or nouns you use, including something as subtle as the difference between words like "opinion", "conviction", "view" and "belief" can give away your political opinions
, and different forms of slang or simply different dialects (with their own quirks in preferred synonyms) may expose different social backgrounds that can be subject to a certain political bias, and thus, depending on the exact details of the language (pre)processing (and things like dimension reduction) and search algorithm used, may inadvertently influence your search results.
A friend of mine recently told him he thought I was in an echo chamber. We were talking about Trump at the time and I pointed out how I felt the guy had bizarre and frequently changing views on many issues - he didn't offer me any reason to assume the contrary, but I think he was triggered by the fact that I started by mentioning some typically left wing topics like LGBT rights and his apparent misogyny. Anyway, it is probably true to some extent; I tend to look to other skeptics and science related websites, and I tend to seek out information critical of other news stories, but that in itself is a bias, and thus it is unlikely to be representative, politically speaking. So there's a definite political bias to my search results, though I pointed out to him that I also get a lot of search results from creationists, climate skeptics, and general quacks and pseudoscientists exactly because I read their arguments as well, and they tend not to be on my side of the political isle. But on political topics what I read is probably very much biased towards the left of the political spectrum.
The thing is, he said this as if he was bias free because he has anonymized his google search (he has an app that shoots random search requests at google periodically). That's a dangerous delusion to be under. I remember how Hitchens (was it on the SGU perhaps?) talked about the differences between American and British newspapers; the main difference was that the British newspapers were upfront about their biases, whereas the American ones pretended to be impartial. I think the moral of the story was that it is better to be aware of the bias in what you're reading, than to think you've somehow escaped it entirely when you really haven't.