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Stress levels can be measured. How an individual responds to stress will vary somewhat, but not because stress can't be measured. How a person responds to stress is a combination of the outward symptoms of stress and the actions of the individual to reduce level of stress. Additionally, how much of a particular stimulus will be necessary to induce stress will vary among individuals, as will the types of stimuli that induce stress.
The tool used to measure level of stress is measuring the amount of cortisol present at the time. Individuals experiencing stress on a regular basis will become more tolerant of stress over time (akin to tolerance in alcohol levels) and show a decrease in actions to reduce levels of stress, but will still show cortisol responses (akin to measured blood alcohol levels).
There are methods to measure effects of stress, such as testing ability at a cognitive level, physical coordination, physiological responses (heart-rate, perspiration, etc), and rater-response questions (i.e. "on a level of 1-10, please rate your stress level now...." and repeated at intervals during testing).
Similarly, with alcohol consumption, there are methods to measure effects of "drunkenness" that fall into the same categories. There is a correlation between amount of alcohol consumed and level of drunkenness, but toleration will affect the slope of the curve and its starting point. Nonetheless, there are measurement tools available for determining level of alcohol in the bloodstream and corresponding effects of the alcohol on the individual -- and the same applies to stress. The reason it may seem without a "concrete form of measurement" to you is because you are conflating two things that are correlated but act at different rate-slopes.
As for your last few sentences, there is no "need for dependence on a higher being to comfort you when you experience fear." Many people in this world experience their lives without it, and are doing just fine. I'd offer the converse statement to yours by saying that the "state of mind" putting people in the "dependence on a higher being to comfort you when you experience fear" is something being taught in our churches these days. But it is not the only way to live life.