Just like most other people I was never really able to make my religious faction happy. ... Is that so, or am I just reading/imagining things that are not there?
You tend strongly toward making assumptions that are not based in the mechanics of the code - the code doesn't think like a person. There is a difference between the "faction's" happiness which is largely a function of the faction leader, and the weighted average of the individual religious happiness factor for the entire population.
Every unit has a religious need; the five needs are also happiness factors along with five non-need elements; each unit ranks\weights its ten happiness factors.
Each unit has two meters associated with religion: one registers how fast the need goes from satisfied to unsatisfied (and the reverse when being recharged); the other shows the level of happiness.
The needs meter discharges and recharges at variable rates. When the meter has discharged to the red zone, the unit enters the religion recharge mode. It then looks for a vacant slot in a cathedral (first) or church (second); if one is available, it claims it and starts to walk to the building - when it enters the building, the meter starts to recharge; if one is not available, it does the default routine - it goes home (or aimlessly wanders) and spends a long time reading its "bible" (check thought) while the meter recharges. When the needs meter is recharged, the religious happiness meter is set to the value of the building's 'Service Quality' rating or next to nothing for the default routine; then the unit transitions to its next mode.
The happiness meter stays at that value until the next recharge routine unless
the unit moves through the religious aura (radiated effect) of a building in the meantime. The cathedral and church have a positive value auras; the pub, cabaret, night club, casino, and distillery have negative auras. Moving through the building religious auras causes a change (plus or minus) in the religious happiness meter.
Most players tend to make two mistakes: a} not enough slots in cathedral plus church buildings because they don't know about the default routine and its negative effects; and b} heavy reliance on the pub and cabaret for entertainment without knowing of their negative effect on religious happiness.