I’ve seen this question pop up quite a few times recently, and the answer is going to vary depending on when you got into fandom and which fandoms you’re in.
You’re probably already aware of the idea of a “ship” in fandom - 2 or more characters that a fan or fans think would be interesting to see in a romantic or sexual relationship with each other.
Back in the 90s in the X-Files fandom, proshippers were fans who wanted to see Fox Mulder and Dana Scully together in a romantic or sexual relationship. Noromos (“no romance” fans) or anti-shippers were fans who wanted the relationship between the two characters to remain friends and colleagues. The whole point was whether or not a particular fan wanted a relationship between characters to be platonic.
The fans from X-Files were in other fandoms too and eventually these terms entered new fandoms. Eventually more terms were developed, such as multi-shipper, which means either someone who has many ships that they enjoy or someone who ships the same character(s) with many people. It often means both.
At this point, it was still about whether or not a fan ships something and to what extent. But then the terms started being used during ship wars.
A ship war occurs when a fandom fights about which ship is “better” or “canon” or “right.” At first, these wars were fought purely on the basis of what was shown in canon. Over time, in order to be right, people on one side or the other of the ship war would bring in arguments about whether the ship was “healthy” or “problematic.” Then terms like “abuse” were brought in. Then suddenly “pedophilia” and “incest” were major topics of concern.
All of these terms are in quotes for two reasons. One, the characters being discussed are fictional and therefore none of these things are actually happening in real life. Two, in order to win a ship war, fans were stretching these terms beyond their usual definitions. For example, in many cultures the term “brother” is used as a common honorific and has no actual familial meaning when referring to a friend, but fans would say the characters saw each other as brothers and therefore the relationship was incest and therefore it was abusive and therefore wrong.
At this point in time, there are still those who see the term “proshipper” to mean someone who generally thinks it’s okay to ship what you want and read what you want and ignore the rest. However, in newer fandoms or fandoms with a lot of younger fans the term has shifted to mean “problematic shipper” - or someone who prefers to ship characters in incestuous, pedophilic, or abusive ways.
The term “anti-shipper” or “anti” has also shifted away from meaning “a person who doesn’t ship something” to now meaning “a person who judges other people based on what they ship.” Anti-shippers are also often equated with people who have difficulty separating fiction from reality, people who harass other fans for what they ship, and people who are strongly tied to American Christian ways of thinking.
The phrase ship and let ship also used to be common in fandom but seems to be less used now. The basic idea of that phrase is, if you don’t like it, don’t read it (DLDR). This used to be easier when fandoms and sub-fandoms were more separated from each other in private communities and independent websites. In the current social media climate, it’s more difficult than ever to separate from each other.
Also, with so many fandoms now using the single website AO3 to host their fic, new users who are less familiar with the search and filter options are seeing things they don’t want to see.
I don’t really have a conclusion here. This is just the state of things as I see it. Feel free to share your own thoughts in the reblogs, as always, but be aware that I’ll be hiding or removing any reblogs or replies that are hateful or harassing anyone - proshipper or antishipper.