We do trust in others to some extent (often to a great extent) when it comes to what we know or understand about our world or universe. The level of that trust is dependent on a number of factors.
Some factors are unreliable. We may trust in something if enough people tell us it is so. Other factors are much more reliable. We will trust in knowledge whose application confirms what we are being told. The latter is even more useful if there is a way for others to confirm it as well.
Science is the latter. The scientific method sets out the ways in which knowledge and understanding can be reliably pursued. Observation, hypothesis, research, experimentation and --most important-- documentation. Showing others your work so that they can replicate it and prove, disprove, or improve it. Keep what works, discard what doesn't. Rinse and repeat, so that over time mistakes and human biases can be gradually filtered out.
Religion is the former. Without an agreed-upon method of determining what is true and what is not, we are stuck at the observation and hypothesis stages, and we cannot progress from there. This is why science can reach global consensus on issues, given enough time. And why religion cannot, and is so fragmented that even specific religions are split into many different denominations, some of which are irreconcilable even though the primary tenets are not in dispute.
What I'm trying to say is that trust is not an equalizer here. Some things are much more trustworthy than others.