People are quite good at lying to themselves about how objective, rational, and scientific their thoughts & opinions are, yes. Science is itself prone to ideology. See people being attracted to beautiful, simple theories.

Well, the point of the scientific method is that it isn't prone to ideology.

If those beautiful theories don't work, then they're abandoned.

The point remains that there are people who strive to avoid cognitive biases and self delusion, see Cartesian doubt.

The claim to be non ideological doesn't always mean the person is the most ideological. It can just actually mean the person is striving to be non ideological.

The scientific method does not give an account of why a given theory must be accepted or rejected. That process is ideological - and no, Popperian Falsification isn’t used, update your understanding of this phenomenon (science) you love so much. Read The Structure of Scientific Revolutions and join us in the post-1960 understanding of science.

To give you a taste: if falsification of theories is grounds for rejecting them, all theories must be rejected at all times. There are always - always - some phenomena that are not explicable with current theories. Much of the practice of normal science is in coming up with an explanation of these phenomena using the current theory, not coming up with new theories. Coming up with new theories is an extremely rare practice not done by most scientists. So how do you tell whether a given anomaly will eventually be described by the current theory, or will remain inexplicable until the formation of a new theory? You cannot. New theories also have many more unexplained phenomena when they are first articulated, since not as much work has been put into conforming observation to theory (if that last sentence seems backward to you, you probably don’t know how science is actually practiced). So what grounds does a scientist have for choosing a new anomaly-ridden theory rather than an old anomaly-ridden theory? The process is in part ideological and has nothing - I repeat - NOTHING to do with the scientific method. Emerging theories are chosen by scientists with a high risk tolerance using not a small amount of faith. And many times this bet doesn’t pan out: the theory eventually dies and considerably sets back their career prospects, as all the time they spent conforming observation to theory (again, the practice of normal science) is completely discarded.

The use of “theory” in the above paragraph is probably different from how you think of the meaning of the word. This is analogous to how new theories work: they aren’t just a refinement of previous theories, they actually explain the world in a novel way using different language, occasionally the same words with wildly different definitions (for example, Newtonian mass vs. Einsteinian mass). The author Thomas Kuhn often uses the word “paradigm” in the way I’ve used theory up above to help avoid this confusion. Incidentally, that book is why the term paradigm became popular.