Everyone has their own moral compass and "deal breakers".
The person in the relationship is the one who decides whether or not they believe their current mate is "the one". Some people believe as long as they're not married they are still on the market.
This one of the reasons why many folks don't even consider couples who live together to be in a "committed" relationship unless they're married.
I believe commitment is based on a couples behavior and not their marital status. There are many people who are married on paper but will cheat in a heartbeat and there are those who have never married but have remained faithful and loving for over 20 years or more.
Having said that I do believe it's possible for someone to be in a long-term relationship which has grown stale but remains "comfortable". Maybe they were out with friends or went on a vacation and met someone who simply swept them off their feet giving them the courage to end what was already a dead end relationship.
Some people treat relationships like jobs. They won't leave one until they have another one lined up.
Men are like sales people in that they don't seek out objections and rejections. Asking someone whether they have a significant other at the start of a conversation is seen as looking for a "no" instead of a "yes" to going out with you. Let (them) volunteer that information.
It is not "unheard of" for someone to realize they are with the "wrong" person when the "right" person shows up in their life.
One famous example of this is Brad Pitt & Angelina Jolie. When they met he was married. Ten years later they have since married and remain happy with their six children. He was only married to Jennifer Aniston for 5 years. Even many who opposed the affair and the divorce have come to accept that Pitt & Jolie are in love as they've watched them over the years including dealing with her health challenges. Timing and circumstances don't always jell.
No man "cares" about another man he does not know. This is especially true if he's genuinely interested in a woman.
It's up to her to tell him he's wasting his time. Nevertheless in regard to your question: "Is it right or wrong to date someone who is in a relationship?"
This begs the question of whether or not one is content being the "other woman" or "other man" as opposed to having someone all to themselves!
Over time getting people to cheat with you causes you not to trust having an honest relationship. You become cynical and may even experience karma.