Are cruise ship harbors and airplane airports really this lax security-wise?

It's hard to answer because you don't really give concrete examples.

Low-cost airlines don't make stop in the middle for no reason at least I didn't experience that yet. What happens is that you buy two flight tickets and instead of flying directly to your destination you make stopover somewhere. Because most low-cost airlines don't have ability to transfer you on your next flight, you will have to exit the airport and enter the airport again going through security and checking in your luggage again.

I don't travel by cruise, but I can imagine the purpose people take cruise is to visit places and not to spend all the time on the ship. Every time you leave the cruise they are going to check your passport and see if you are allowed to enter the country.

The answer is no, the airlines and cruise companies are not that lax with security.

First the flights, all people in a plane have been checked and are deemed safe enough to be on board, their carry on luggage checked. When they have to make an emergency stop they mostly have to stay in a restricted area and are not allowed to wander of.
But when there is a longer stop and the airport they are does not have the facilities they are mostly brought to a hotel that can handle them.
In some cases the country they land do tell the airline/airport officials that the passengers do not need such restrictions and are allowed to wander freely. One reason they allow such is that the government is pretty sure the people had no expectations for a stop there and will not want to be left behind when the option for resumed travel will open up. And in many cases only those people who would be allowed in without visa or who would get visa without too many questions are allowed to wander.
For scheduled stops, where the passengers get off the plane, into the country to return to the airport when ready for the next part of the travel, they have to have all needed paperwork for the country they get off the first plane. If planes are landing on other airports than planned, they mostly try to use other airports which are in the same country or at least in a country where most of the passengers will be allowed to enter. When in a different airport or even country from the plans, the airline or the airport officials will make sure that those people without the right paperwork will be allowed to travel or will be restricted till they reach the country their papers are valid for.

In case of the cruise ships, mostly before boarding you go through a security check and a passport check. When you come to a port, the officials there know that you meet the restrictions they set for cruise passengers. If you do not meet those restrictions (i.e. do not have the right visa) you are often not allowed to join the cruise at all.

In some cruise ports all passengers going on land will be checked, when not all passengers have visa. When with a Baltic Sea cruise, Russia, for instance, you may be allowed to join a coach party without a visa for the country. In that case you are kept with that party and not allowed to stray off. Others who have visa are allowed off board and do their own thing, but their passport and visa are checked before they are allowed to get off.
The other ports on this cruise were all in the Schengen zone and all passengers were required to have the needed paperwork for entry to that zone, either the right nationality, a visa replacing stamp in their passport or the right visa.

All ports that regularly have cruise lines stopping will have some system, mostly for the whole of the country and all cruise lines, but exceptions can be made.
If a cruise ship have to stop at a port where they do not have such systems, the cruise company and the country involved with come up with a way that will work.

Recently several cruise ships had to port with COVID-19 sufferers, often in ports the line would not usually use. The passengers were taken from board in numbers which the local system could handle, into coaches and on to the hotels or airports for further isolation or travel. Where visa would be needed, those are either given or the people who would need them kept under the eyes of officials or not given the option to wander. The exact version will depend on the country where they are taken off the ship and the nationalities involved.

When traveling by commercial, low-cost airplane flights to a location, they frequently make a "stop in the middle" for some reason, forcing all the passengers to exit the plane, wait around at or near the airport, and then board another plane, possibly many hours of waiting in between

Flights don't just stop "for some reason" as if it's some kind of mystery. Time the plane is on the ground is time it's not carrying passengers, and therefore not making the airline any money. There are always specific reasons to stop. Sometimes particularly long routes will have stops for fuel, and there are even some flights which serve multiple destinations in much the same way as a bus or train, but those stops are generally rather short. Far more often, the reason is that you're talking about several different flights. For example, Swiss don't fly from Hamburg to Barcelona, but they do fly from Hamburg to Zurich and from Zurich to Barcelona. So if you're in Hamburg and you want to go to Barcelona, they'll be perfectly happy to sell you a ticket from Hamburg to Barcelona via Zurich. Passengers might choose that option because it's cheaper, or at a more convenient time, than flying direct (or, with other destinations, because there are no direct flights available).

During this time, as I understand it, the passengers/travelers are allowed to freely exit the airport and go around town in whatever city in whatever country they are "middle-stopping" at, as long as they come back in time for the next departure?

Yes, as long as you comply with the standard immigration requirements (depending on nationality you might need a visa, for example).

Isn't this a bit strange security-wise, considering the rigorous security (or perceived security) measures they have when you actually board a plane or (I thought) exit the airport to enter the country/city?

When you leave, you go through the same immigration procedures as the people who have that airport as their final destination. When you return to the airport you go through exactly the same security as all the people who are preparing to board their first flight. At many airports that means that while you are allowed to leave between flights, there's no point unless you have at least 4-5 hours (or even more in some cases) between flights.

But how is this possible? I thought airports and harbors these days had tons of "security theatre" nonsense, with tons of "red tape", making it an absolute pain to deal with, and something to avoid at any cost? Or is this somehow ignored for cruise ship people? They just show their wrist band and the people go: "Sure! Enjoy your few hours here!"?

See this link posted by @Traveller in the comments for an example of how immigration requirements are handled on cruises. The details will vary between operators and destinations, but it's broadly the same thing: passengers have to supply the cruise operator with details of their passport and other required documentation. The cruise operator makes those details available to immigration at the cruise's destinations. The passenger's documents are checked when they first arrive at the departure terminal to make sure they have the documents they claim. If you don't have the documents required to enter the cruise destinations, you won't be allowed on board.

At the destinations, people don't typically need to pass immigration, as checks are performed remotely based on the documents which were already collected. On returning to the ship, each operator will use different techniques but there's an ID check of some sort to ensure that you are indeed one of the ship's passengers.

And the same goes for airports when they "stop-in-between"? If so, why is security vastly different for people who (maybe) will only stay there for a few hours?

As I said earlier, you face the same security procedures on your way in and out of the airport as all the people who are just taking one flight.

Can't they also hurry up and commit all kinds of crimes in those hours? I don't get it.

Can't you just commit all kinds of crimes in the few hours before taking your first flight of the day? I don't get what you think stopovers have to do with this.

Something about this doesn't add up to me. It seems like you can "trick" or "bypass" your way into visiting all kinds of places just by taking a cruise or flying cheaply (the flights that stop on the way seem vastly less expensive money-wise), but something tells me that they must have thought of something which I haven't.

Buying tickets to places is not "tricking" your way into visiting them. Visiting multiple places is literally the entire point of a cruise (ok, sure, it's not the entire point - but it's generally a major selling point and the primary purpose for many passengers). With flights, stopovers are often just an irritation that you put up with because it saves money or avoids having to waking up at 3am. But yes, occasionally it can be a nice bonus to have a few hours to explore somewhere.