Every decision we make as scientists are influenced by our ideologies. In every step of the research process, we are faced with choices. Despite our theories being well-grounded in the findings of our predecessors and efforts we make to maintain objectivity, our own ideologies influence the research question itself, our operational definitions, our selection of a study population, our interpretation of the findings, and the reporting of the findings.
Even if we believe we have achieved perfect objectivity (which is impossible because we are human) science can still not be separated from ideology because someone has to make the subjective decision about what findings should be presented to the general public and which should not.
To provide clarification on a few of these points, let me give you examples.
Imagine you are a scientist that wants to test a new drug's effectiveness on killing cancer cells. The very fact that you want to study this implies that you believe cancer is a problem that should be changed. As absurd as it might sound (who wouldn't want to cure cancer?) the point is the same. By selecting this as an important research question, you have made a subjective decision that reflects your ideology.
Next, suppose for a moment that you are a psychologist that wants to find out if parenting styles influence children's self-esteem. What will you include as 'parenting styles'? What does 'self-esteem' mean? How do you measure 'self-esteem' or 'parenting styles'? Which types of children and parents will you include in your study and which types will you exclude? Every time you answer one of these questions you make a subjective decision.
Even if you decide to use a measure that someone else has developed, you make a judgment that the measure you have selected is superior to some other measure available.
What happens if your findings do not align with your theory or your hypothesis? Some unethical researchers may choose to alter the data to prove their point.
What if you have one case that doesn't fit with the rest, an outlier? Do you exclude it or include it and risk the possibility of skewing your data? Again, you make a subjective decision. Your training, beliefs, and ethics will determine your actions.
Finally, imagine for example that a study finds a strong correlation between news broadcasts and anti-Semitism? (this is a fictitious example, of course) While the research findings might be published in a peer-reviewed journal, it is likely that those in power at the news station will not want this finding made public. If they report on it at all, they may misrepresent the actual findings to serve their own interests.
Thus, from all these points it is logical to conclude that, from the start to the finish, it is never possible to completely separate science from ideology.