By: Jason Woodward //
“Mormonism is truth … The first and fundamental principle of our holy religion is that we believe that we have a right to embrace all, and every item of truth, without limitation or without being circumscribed or prohibited by the creeds or superstitious notions of men.”
“Have the Presbyterians any truth? Embrace that. Have the Baptists, Methodists, and so forth? Embrace that. Get all the good in the world, and you will come out a pure Mormon … One of the grand fundamental principles of Mormonism is to receive truth, let it come from whence it may.”
— Joseph Smith 
Thanks for the question! And although you asked specifically about evolution, the theme of “what I believe vs. what I think I ‘should’ believe” is one that touches a much broader range of topics. A quick dive into the past might help illustrate this dilemma — and hopefully help you come to a conclusion:
For thousands of years, the worlds of science, philosophy and religion all thought that our Earth stood at the center of the universe. This idea, known as the geocentric model, held that all heavenly bodies rotated around the Earth while it remained completely still. Based on past teachings and the crude observations they could make at the time, it made perfect sense. And the closer the idea became tied to biblical verses, the more it entrenched itself into the religious worldview of the day: we were God’s most important creations, everything else was made for us, and we existed at the center of it all. It was a grand vision of man’s place in the universe, and for some, this scientific belief practically became religious doctrine.
The geocentric model of the universe.
But with the invention of the telescope, everything changed: astronomers saw that Jupiter’s moons orbited Jupiter, not Earth. They learned that the other planets orbited the Sun, and that we did too. The work of men like Copernicus and Galileo dismantled the scientific credibility of the geocentric model and replaced it with the heliocentric model — one where the Sun actually formed the nucleus of our solar system, and where the Earth moved around it instead of vice versa. Turns out we weren’t at the center of the universe after all.
But despite this overwhelming flood of new evidence about the true structure of our solar system — and the completely non-spiritual implications of the discovery — the Catholic Church proclaimed that the heliocentric model was “false and contrary to Scripture.” The Church simply could not let go of the belief that the Earth was the center of the universe. As a result, Galileo was convicted of heresy because “his position “contain[ed] various propositions against the authority and true meaning of Holy Scripture;” and he was eventually placed under house arrest for the rest of his life.
Although Galileo tried to explain that there was no real conflict between the scriptures and the heliocentric model — that the Biblical writers weren’t making scientific claims at all, but spiritual ones; that they wrote from a limited perspective; that many stories were told allegorically to teach specific principles; that this didn’t change our status as God’s creations; etc. — he never lived to see a harmony between science and scripture. In one of his letters, he lamented the fact that many of those who opposed his discoveries had refused to even look through a telescope for fear of what they might see. Instead of opening their minds to the possibility of new truth, they stubbornly shut their eyes.
So returning to your question — it’s true; some Mormons do share this same skeptical view of scientific discovery. In many cases, people read scientific details into spiritual teachings, unwittingly committing themselves to defending something (like geocentrism) that was never part of the spiritual teaching to begin with. And if the Galileo story teaches us anything, it’s this: if you try to put words in God’s mouth, you’re gonna have a bad time.
But as the introductory quote by the Joseph Smith makes clear, if any Christian religion offers a place to embrace all the truth science has to offer, it is Mormonism. Our theology does not demand that the earth is only 6,000 years old, or that every inch of its surface was entirely covered by water during a global flood — even though some may commit themselves to those interpretations. At its core, Mormonism teaches that scientific truths enhance our understanding of God and His divine plan for each of us.
In the words of Elder Dallin H. Oaks, a member of the Quorum of the Twelve Apostles:
“[We] sometimes encounter what seem to be conflicts between the respective teachings of science and religion … Some try to deal with apparent conflicts by compartmentalizing science and religion — one in one category, such as Monday through Saturday, and the other in another category, such as Sunday.
That was my initial approach, but I came to learn its inadequacy. We are supposed to learn by both reason and revelation, and that does not happen when we compartmentalize science and religion. Our searchings should be disciplined by human reason and also enlightened by divine revelation.
In the end, truth has only one content and one source, and it encompasses both science and religion … Latter-day Saints should strive to use both science and religion to extend knowledge and to build faith.”
— “Life’s Lessons Learned: Personal Reflections,” 55–60
In other words, true religion and true science are never at odds. And although scientific hypotheses come and go but the gospel stays, I try to be careful about gluing the “Eternal Truth” label on things too liberally. Modern revelation has provided us with all the knowledge we need to return to our Heavenly Father — and not a single thing more. Even if we don’t have every answer, we have the most important ones.
I’m not telling you what to believe regarding evolution. But when it comes to such issues, I find it best to remain open, always ready to gaze into the telescope in search of new truth, regardless of the source. In a word, the answer to your question is YES. Or in a few more words from the prophet Joseph Smith: “We should gather all the good and true principles in the world and treasure them up, or we shall not come out true Mormons.” 
Still don’t believe these kind of Mormons exist? Maybe this video from the official Mormon YouTube channel will change your mind. Yeah, science!