Disclaimer: A single newbie can ask more questions than ten grand masters can answer.
It is obvious that most of the time, you would not want to share a dogma. E.g., sharing Writing defeats the purpose of the card (getting to Age 2 several turns ahead of your opponent). However, there are cases when sharing is... okayish to good.
1) Most certainly if your opponent cannot share the dogma due to other dogma prerequisites, e.g. Mathematics or Currency with an empty hand, or Paper with a single card in both green and blue stacks.
2) When a dogma benefits you way more than your opponent, say, playing Masonry for Monument against a castle dominance when the opponent has less than 4 cards. The definition of "way more" is, of course, a big question each time.
3) A special case is, I think, splaying, if it allows you to gain a dominance in an icon and play another (or the same) dogma unshared.
4) When sharing is likely to hurt your opponent. Cases like Sailing when your opponent is well into higher ages but for some reason there's a single "1" hanging there. An edge case may be Alchemy if your opponent has a large dominance in castles (9 or preferably 12) since the probability of drawing a red will be pretty high for him and the card can effectively play as "I demand you return your hand".
Of course the decision to share or not is dictated by the actual game state and the edge cases may and will be multiple. What I attempted to put down (and would ask stronger players than me to expand) were some general guidelines.