Humans are the only rational creatures on the planet, so in large regard the YES to this question is based on the assumption that we wish to keep ideology and science in individual compartments.
It should be entirely possible for a Muslim, a Hindu, an atheist, a Buddhist, and a Jew to arrive at similar conclusions when investigating a phenomenon in our natural world.
A chemical reaction does not know or care what your ideology is. A nuclear weapon will explode the same way for all. A new drug will work a similar cure (casting aside placebo effects) for all worldviews and faiths.
While it’s true that in some regard a person’s faith/worldview may leach into their work, science is not based on religion; it’s based on observation, hypothesis, experiment, and conclusion.
To make this theoretically possible goal reality, the science community must adhere to some universal standards of what constitutes evidence and facts. Those who will not or cannot practice legitimate science hinder all advances in knowledge: the educated community must regulate these people whenever possible by correction and peer pressure. The goal should never be to force conformity in results but rather in accepted procedures for determining them.
If this is done, we won’t have the types of abuses of the past such as the Nazi eugenics ideology. These policies came about from a skewed agenda which worked backward from a decided conclusion. Of course the wicked government of the time made many of these ideas compulsory. This is perhaps the one example where the ideal system will run into trouble, so this essay assumes a democratic society in place.
An example of faith interfering with science comes from present day. There has been a movement over the last 30 years for Creation Science practitioners to weave very questionable scientific procedures into the public discourse to cast doubt about evolution and the age of the earth.
The arguments presented are based on a belief that the Earth is only 6,000 years old. They obtain this very low number by literally applying the Bible to their science.
One cannot apply unprovable faith claims into the scientific realm; indeed the Bible itself says clearly that faith comes by hearing and hearing by the Word of God.
This means no amount of science will ever be able to prove God: it also means that you cannot take a predetermined conclusion (the Earth is 6,000 years old because the Bible says so) and work backward from there to cherry pick only the data that fits in.
The charge has been made that evolutionists do the same thing; but this is false. An honest examination of history shows virtually all scientists in the 1600s believing humans as created specially by God: not only because of a Christian influence in society but more importantly because there was no evidence against it.
It was only when observations began to illuminate new evidence that questions arose. It took several centuries for the scientific community to change its mind about our origins. It was not because of some atheist plot: but because the facts no longer supported a special creation paradigm.
So the problem with ideology and science intermingling is that the natural human tendency will be to skew the data to fit into the belief perspective at the expense of the observed facts.
They can be kept apart, but only by diligent and consistent application of good methods, and professional self-correction of errors as they creep in.
