Is it permissible for a Muslim to adopt the preponderant opinion if there is another more cautious opinion, and is it recommended to adopt the more cautious opinion in all cases, or only when there is a significant disagreement and two strong opinions?

The basic principle is to act according to the strongest opinion among the sayings of the scholars regarding disputed issues. Taking into account the differing opinions and exiting from the disagreement is commendable, according to specific guidelines. Therefore, there is nothing wrong with someone who adopts the strongest opinion, nor with someone who adopts the more cautious opinion, provided that the conditions for exiting from the disagreement are met. Among the most important of these conditions is that the differing (more cautious) opinion should not be extremely weak.