Genuine religion and the direct natural genius known as 'faith.'
Reasons to distrust science:
1) Getting itself trapped inside of an inescapable arms race that has shed more blood and wasted more treasure than any other human endeavor;
2) Producing and failing to secure machines of mechanized death leading to world wars and cycles of genocide;
3) Presiding over the advent and use of weapons of mass destruction upon civilian populations;
4) Constructing a global system of pervasive poisoning called 'mega-industry' that has taken us from a pristine natural world to massive environmental destruction and hopeless economic addictions to poisonous industrial substances;
5) Squandering the bulk of the world resources immediately on comic book nonsense before anyone even has a chance to consider how to distribute them more equitably in the interest of world peace. This now includes 'spider god' cults and space travel scams into the Biblical 'abyss,' (Luke 8:31, Luke 16:26, Matthew 8:12, Revelation 9), constructing 'world-wide webs' and 'social networks' using global infrastructures of lines and fine threads pulsing with artificially produced images, sounds, and simulated realities, (even measured in 'bytes'), all meant to intoxicate and disseminate public spin and lies, leading to the abandonment of ethics, morality and otherwise obvious naturally installed divine processes and Laws. Using this mass intoxication, (with obvious effectiveness given the number of 'science' respondents to your question), to trick people into believing in absurd narratives of cosmic meaninglessness, historical revisionism ironically, presented through the same grand and unmatched institutions of academia and social models, (including the original 'university' system), that were invented and defined by religion, (not atheistic science), which unjustifiably castigates religious thought and contributions, (why are we still attending 'universities' at all if science is 'superior?' Shouldn't we have something new and better by now?).
6) Using public spin once again to cover up waves of lineage deaths and irreversible genetic damage being caused by poor and constantly shifting understandings of chemicals and drugs. Included in this nightmare are inescapable addictions, waves of fatal overdoses, gender confusion, psycho-sexual sterility, physical sterility, widespread negligence and needless accidents, sudden inexplicable violence, exponentially expanding asymmetrical violence, 'fringe science' being conducted in the streets of lawless sprawling government sanctioned ghettos supported by oppressive government taxation under threat of deviant rape, torture or other high felonies being used to maintain massive incarceration systems routinely employed to forcibly recruit new members into criminal gangs representing modern slavery, in addition to other disguises like 'human trafficking,' 'state wards,' and 'illegal immigrants,' all while proclaiming slavery to be 'officially abolished' and blaming religion for having 'enslaved' us so mercilessly in the past.
Under religious authorities and agencies of direct natural genius:
1) Human authorities presided over a pristine natural environment rather than a pervasively poisoned one;
2) An acknowledged social duty to protect women and children through the vigorous defense of maidenhood and absolute monogamy, holding back the tide of tens of millions of needless and torturous deaths from unprecedented diseases with no cures and only economically inaccessible torture treatments as 'remedies.' Trust in nature's capabilities, cycles and grander purposes even during outbreaks of disease, containing the damage to one generation of early deaths while receiving multi-generational gifts of immunity, natural moral behavioral reinforcements, generational lessons and perennial wisdom, rather than only wild experimentation with dangerous substances leading to lineage deaths, lessened immunity and irreversible genetic damage.
3) The undeniable and continuing world standard of artistic and social genius, not remotely approached since, (mostly because the exhibition of personal genius does not happen during states of perpetual war and the ongoing prosecution of arms races, which have been happening since the inception and adoption of atheistic science);
4) The proper securement of all weapons from the hands of fools, rather than the unrestricted sale of death on the open market to the highest bidder;
5) The highly restricted and very public use of extreme violence directed at a handful of public insurrectionists and evil agitators, rather than the public legislation of 'tolerance' and the pervasive spread of evil, violence and death, even the ceaseless and needless deaths of infants and toddlers by the thousands, (including being horribly crushed and burned alive), all excused by the word 'progress.'
6) The formation of all grand and worthwhile institutions, (including the first 'university' system), never replaced or emulated since, only infiltrated and co-opted by atheistic secularists;
Science is responsible for every unnatural death and drop of spilled blood on the earth. There is no such thing as a 'religious' deadly weapon or process. Without the contributions of science and its explorations into forbidden knowledge, (including its hypocritical quasi-religious precursors), even in its most extreme form, religion only engages in vigorous public debates, ignites inspired social movements, inspires ingenious commerce and art, competes in the exhibition of personal genius, breathtaking architecture, superlative dynamic education, the protection of time-honored human virtues, the preservation of meaningful and purposeful narratives of existence, holding back the tides of existential dread, pervasive hopelessness, suicides, murders and all other social ills.
There really isn't any debate which one should be trusted more. The only reason science continues to earn anyone's trust at all is because it also happens to be the source of a mass psychological drunkenness that makes it seem impressive, constructive, promising and powerful---but only to those properly spun into a web of lies and all-pervasive Hollywood hokum to be exsanguinated in due course along with all of the other hapless victims of the doomed spider god named 'progress.'