Religious faith can have different meanings depending on the context and perspective e.g. for some it is just a way of life or a support system e.g. people who experienced trauma and grief may seek comfort, support from a community, and way to come with terms with what happen and find new purpose possibly like the Ukrainians you mentioned above.
Otherwise how about faith in yourself/spouse/kids? Optimism? Hope?
Your concept of trust and faith seem different on paper (one is confidence in something based on evidence or past experience the other is belief without requiring evidence or proof) but in practice I think they have a lot in common. We know that its not information and understanding that drives the average joe political\ethical belief system, so isn't it fair to say that the vast majority of people political views are faith like blind trust and fallback to familiar dogmatism they were raised on?
I believe that what you really have an issue with is religion resistance to change.
It's more interesting when you realize Science predates the Scientific Method.
More so when people realize our epistemic limitations and how often people claiming facts are widely over-reaching with enthusiastic interpretation. Especially in social science which deals with human emotions and behaviors and involve numerous variables that are often unpredictable or beyond our control.
Many social issues are
wicked problems characterized by complexity, uncertainty and lack of clear cut solutions, these include things like poverty or climate change, we all know they exist but we don't know what the best way to solve the, only faith-based approaches that involve subjective perceptions of situation, values, needs and wants.