Wikipedia's definition of soap opera is obviously flawed. If it was a perfect definition of soap opera you wouldn't have any questions about which shows are soap opera and which are not.
Of course, it's much easier to see that a definition is flawed than to to come up with a better definition and very hard to come up with a flawless definition (or to be able to tell whether a definition is flawed or flawless).
So let's start with Wikipedia's definition of soap opera and change it a little.
Wikipedia's definition of soap operas is:
A soap opera is an ongoing drama serial on television or radio, featuring the lives of many characters and their familial, platonic and intimate relationships. The term soap opera originated from radio dramas being sponsored by soap manufacturers.
So I might change the definition to something like this:
A soap opera is an ongoing drama serial on television or radio, primarily featuring the day to day lives of many characters, who are more or less ordinary people, and their familial, platonic and intimate relationships, in more or less ordinary situations, and created to be primarily an example of the soap opera genre. The term soap opera originated from radio dramas being sponsored by soap manufacturers.
I added primarily to show the main focus of a typical soap opera, and I emphasized that the characters and the situations they are in are more or less ordinary - in some soap operas more or less ordinary than in others.
In recent decades more and more dramatic programs in the USA have become more serialized and less episodic. Thus they come to resemble soap operas in some ways. But those shows are often primarily intended to be examples of the crime, fantasy, historical, horror, medical, police, suspense, spy, science fiction, western, etc. genres, and not primarily soap operas.
I added "created to be primarily an example of the soap opera genre." to help distinguish shows that could be considered "true" soap operas from other shows, shows that are like soap operas but are primarily examples of other genres like crime, fantasy, historical, horror, medical, police, suspense, spy, science fiction, western, etc.
For example, most Star Trek series are episodic, with each episode being a separate story. In fact, I favor the theory that most episodes of most Star Trek series happen in alternate universes of their own, separate from the alternate universes of other episodes within their series.
But a number of Star Trek series had continuing story arcs spread out over a few or sometimes many episodes and thus seemed much more serialized than the original Star Trek and more like soap operas than like pure episodic shows. But they differ from soap operas in being partially episodic and partially serialized instead of totally serialized, and by being primarily science fiction space opera shows where the characters are in situations which are certainly not ordinary for the viewers in the present and often get highly unusual even for the future society the future characters live in.
The main focus of even the most serialized Star Trek series is science fiction space opera type events, and the day to day daily activities of ordinary people, even the ordinary people of a future society, are not the prime focus, as they would be in a true science fiction soap opera.
Each season of 24 (2001-2010) was extremely serialized, telling of events in a 24 hour period in a series of hour long episodes. But 24 (2001-2010) was about political intrigue, action, counter terrorism, espionage, etc., and 24 (2001-2010) is described as "an American action drama television series" in Wikipedia,not as a soap opera.
One important method of telling a soap opera is its broadcast schedule. In the USA a prime time soap opera, like Dallas, would broadcast first run episodes once a week for about twenty odd weeks each year, and have reruns the other weeks of the year, with a schedule very similar to those of prime time shows that are not soap operas. But daytime soap operas tend to broadcast first run episodes five days a week, 52 weeks a year, with no reruns.
Some soap operas were broadcast live, and so viewers got to see every production blooper made in every episode, though that is not a characteristic of prime time soap operas.
And genres are not exclusive. It is perfectly possible for a series to be an example of two or more genres at once.
A famous example is Dark Shadows (1966-1971), mentioned by Raj in his comment, a daytime soap opera that can also be considered an example of the suspense genre, sometimes the crime genre (a lot of crimes were committed), sometimes fantasy (there was a lot of magic), horror (vampires and werewolves, etc.), science fiction (time travel and alternate universes, etc.), and historical (characters traveled to past centuries and stayed there for months at a time), etc.
Or some people might claim that Dark Shadows (1966-1971) was an example of the Dark Shadows genre, being a genre to itself.
Another soap opera example is Passions (1999-2008) which was a soap opera with strong supernatural elements. One of the main characters was a witch, Tabitha, who was so powerful that she brought a doll, Timmy, to life, & he become another character on the show.
(curiously, according to this site, Passions (1999-2008) is in the same fictional universe - imaginatively labeled as Group 10 - as a few other series, including all the Star Trek series.)
Another famous example is Get Smart (1965-1970), a situation comedy which was also a spy series. The protagonists were in deadly danger in almost every episode, and killed a lot of people, which is very unusual for a situation comedy.
So it is possible for a series to be both a soap opera and a horse opera, a soap opera and a space opera, a soap opera and a spy drama, a soap opera and a medical show, etc., etc., and some people may be able to suggest a number of examples of such hybrid, multi-genre series.