It's the same thing that an intuitive person could do by looking at body language, reading between the lines of what someone said or didn't say, or listening to their hunches, only more so.
We don't know when we're being studied or observed, but there is only so much a person can tell about us by watching us normally without technical aids or a higher level of access. I suppose it could be considered an invasion of privacy, but maybe that's regarded in extreme circumstances like entering a house without a search warrant because you hear screaming. If something is going on, a captain needs to know for the needs of the many on his ship and in the Federation/Starfleet.
I going to disagree with this.
An intuitive person is observing without intruding. They are observing what is being broadcast or put out there for everyone to see. Sometimes an intuitive person gets it wrong.
In contrast, a Betazoid's ability is intrusive. It intrudes on the hidden thoughts and emotions of others. The difference would be seeing a present or a box and actually peeking inside the box.
Because the above are conscious actions taken to trap someone. Betazoids are using what is a normal sense for their people. To ask them to turn it off would be like asking a human to turn off their hearing.
This is a good point. Similar to someone accidentally picking up the phone and hearing private conversations vs. intentionally eavesdropping. If Betazoid's senses are passive and cannot be regulated or turned off, then there is no intent behind Troi picking up on emotions.
However, even if the ability is passive and cannot be turned off, ethics might dictate the Betazoid keep their big mouth shut. Choosing to speak or keep silent is an active decision, not a passive ability. Revealing the thoughts or emotions of another individual is a choice.
That's where the ethics ultimately comes into play. Is revealing private information ethical? If private thoughts are private, and a Betazoid (or some other telepath) learns this private information by accident or without intent, then what gives them the right to share that information? If a telepath needs to actively choose to read these thoughts or emotions, what gives them the right to peer into another person's private thoughts and feelings without consent?
Ethics comes down to consent, control, and choice. If a person can control their ability to learn information that would otherwise be private, and if said person did not receive consent (or legal authorization such as a warrant), then is it ethical for that person to choose to learn and/or reveal that information?