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Proship = not harassing or judging people over their tastes in fiction
A proshipper is someone who supports romantic pairings in fictional media that are considered problematic, and also supports the creation of fanworks based on those pairings.
There is no universally accepted definition of "proshipper", but proshippers generally disagree with "antis", who believe that taboo or abusive sexual content in fiction directly influences the actions and views of those who consume it. Proshippers may disagree with antis for a variety of reasons, including completely rejecting the idea that fictional media influences behavior.
Pro shippers are people who believe that people should "ship and let ship", meaning whatever a person ships is fair game. The opposite of pro shippers, "antis", are people who think that there are limits to shipping that should be obeyed.