Sit down, nonnie, this is going to be a long one!
I need to start this by saying that I would be someone classed as a proshipper. I don't necessarily label myself as such though and when it comes to the drama around this, I think both sides can be terrible and toxic, but because of my views I would be labelled by an anti as a proshipper (or proshitter because yes, that is how childish they can be).
A proshipper believes that fiction does not affect reality on a 1:1 ratio which will often be shortened to be "fiction doesn't affect reality" which doesn't actually represent the views of many people who are given this label. However to place it simply, a proshipper would not care who you ship: age gaps, toxic relationships, incest of any kind etc. because they believe that what you enjoy in fiction doesn't not indicate the type of things you would enjoy in a real life relationship.
An antishipper, as you can guess, is the opposite, they believe that fiction does affect reality and that your taste in media can be an indication of what you enjoy in reality.
This has led to the words problematic, pedophile, abuser, groomer and the like to be thrown around in fandom like they're candy and not serious accusations to accuse someone of and has watered down the words to the point that when someone is claimed to be, say, a pedophile, it makes people think "are they really or did they just like a "bad" ship" which obviously is a very big problem.
Now, there is nothing wrong with being uncomfortable and even downright hating ships that have incest/pedophilia/abusive aspects and in fact many people who will say "ship and let ship" (a common phrase used by proshippers) will hate them too. I can't stand these types of ships personally and will block anyone who has them as they make me extremely uncomfortable, however I won't harass people who have them either which is a common tactic of the antishippers.
You don't know the people behind the ship, plain and simple. Many proshippers with these darker ships have even had to share how they were/are victims of what they're being accused of and how they use such ships to help them come to terms and take control of their own trauma.
Or they could be dangerous people (though I don't know what the percentage of people that would be) which is why I will never understood why antis will ask each other to put themselves in danger to harass these people.
My issue with antishipping is that any ship can come underfire and be labelled a proship by these people. I've seen things be called proships for people who have shared the same body in funky soul shenanigans, I've seen them been called that for people who look too much alike, I've even seen it for age gaps that are completely normal in real life.
There is no common consensus for what is a proship, it's become a word to mean "ship I don't like" for many and is used extremely often to shut down ships and people shipping it.
I'll use a proship of mine as an example and one that is often the target of antis on twitter. I've made it very much aware I love the relationship between Osamu Dazai and Sakunosuke Oda from Bungo Stray Dogs. Now Oda was 23 when he died, Dazai was 18 years old. For many, this 5 year gap was too inappropriate for them because Dazai was a "minor" at the time of their friendship. This got even worse when the author revealed that Dazai and Oda met when Dazai was 16.
It doesn't matter that to many antishippers that people who love the ship enjoy it with both characters of adult age (it's very rare you see anyone shipping them when Dazai was 16 and even at 18). Because he knew Dazai when he was a minor, their relationship cannot change at all, Dazai will always be viewed as a "kid" by Oda (despite that having never been their relationship) and if you ship them you are a pedophile.
Yes, that is the word that is often used. You get called a pedophile for shipping two characters who are legal age.
Now, can the age gap in the ship be uncomfortable to people? Sure! Can the potential power imbalance be uncomfortable too? Yes, it can and I have many ships where I find myself in the same boat. However instead of the antis of the BSD fandom blocking and avoiding this content, they will accuss creators for the ship of being horrible thing and will harass and insult them.
This is why I called it a cult. You saw in the post I just made how a person had to ask if something was okay? They didn't go "I think this is uncomfortable so I won't enjoy it and avoid it" they had to make sure that it was okay with the hivemind to like it another way. At this point antis aren't thinking for themselves, they're doing what they think others expect of them.
What's even worse is that some anti communities have been shown to have been run by actual predators who are preying on the minors that flock to them for "safety" from these "dangerous" ships.
There have been classic textbook abusive behaviour from these communites such as isolating minors from "dangerous" adults and making them feel like they're the only people they can trust. It's often believed that predatory adults will use "proship" content to make minors trust them but it's just no true, a predator will use anything that will endear them to their victim and that includes antishipping.
It's extremely dangerous and terrifying to see.
There also the fact that many antis care more about the lives of fiction people than real people. I will see them celebrate and laugh at "proshippers" who feel suicidal or have committed suicide, even going as far as to tell them to do it. It's horrifying.
I'm sorry I've gone more into the antishipping community than the proshipping community but that's because I'm genuinely terrified of the antishipping community. They make fandom a terrible and toxic place to be in.
For many years, proshipping was the standard to the point it hadn't even been called it. It's only recently the anti community started to rise, bringing with them both insane purity culture and abusive/bullying behavior to anyone who won't conform to their standards.
Please, everyone stay safe in fandom.