Have you ever wondered what the gender-neutral equivalent for the word “knight” or “dame” is? Chances are, no, probably not. But I have, and that's what I'm going to try to answer anyway.
Firstly, why does it even matter? Using gender-neutral language is a good idea, even for cisgender people, because gendered language can allow discrimination based off of some peoples' perception of gender-roles. Equality is always a good thing, though this mainly discusses an explicit non-binary word. Maybe you're writing a fantasy story, or role-playing with friends. Chances are, if you're doing any of those, there's a 50/50 change you're queer. If anyone involved is non-binary, this question will need an answer. Of course, there is still real-life royalty that does, in-fact, knight people; but, what are the chances that any of them actually read this?
The simplest solution would just be to only use one word regardless of gender. The word “dame” is certainly gendered, but the word “knight” is a little more ambiguous. Why not just call all who receive this honour a knight: men, women, and enbies.
What about systems that don't do this, and instead use different gendered words? These systems are less ideal, but it does still raise the main question — if “knight” is masculine, “dame” is feminine, then what is the non-binary word? For a system that calls everyone a knight, regardless of gender, there is no problem with using that word for enbies too. But making enbies use the word “knight” or “dame” when they very much have implications of binary gender is not okay. So, what's the alternative non-binary term?
Some Google searching told me that the most common solution is to use the word “ser” as a gender-neutral option, but I don't think that this is that good. Firstly, it's just way too similar to the word “sir”, both in spelling and pronunciation. Also, where does the word “ser” come from? Well, it's Dutch — Middle Dutch, to be specific. The modern terms are gendered: “meneer” for men and “mevrouw” for women. “Ser” may have been a good word in Dutch, but I don't believe it is in English.
The reason that the Dutch word “ser” is so similar to the English word “sir” is not a coincidence. They are what are called cognates. A cognate is simply when two or more languages have words that are very similar, and mean similar things. An example of this would be how the Spanish word for “family” is «familia». So, in other words, the reason that “sir” and “ser” are so similar is that they are sort of the same word; or, a least, they used to be. Cognates can be spelled the same, and mean the exact same thing, but “sir” and “ser” are not examples of this. The English “sir” is gendered, even though the Dutch “ser” isn't. Using the Dutch “ser” in English alongside “sir” is better than nothing, but I believe there's an even better solution.
You may have realized that “sir” and “knight” are different things. The word “sir” would be put in front of the name of a knight. These kinds of words are called honorifics. The most common honorifics are just “Mr” and “Ms”, which you've definitely heard before. “Sir” and “Dame” were originally just honorifics someone could use after being knighted, but now “sir” is just used as formal versions of “Mr”. The discussion of a non-binary honorific is actually a discussion that many people are having, so I'll just refer you to the Wikipedia page Mx (title).
So if “sir” and “ser” are honorifics, not generic nouns, does Dutch have another word for knight? Yes, Dutch uses the word “ridder” as a generic gender-neutral noun, meaning knight or dame. This was the case in Middle Dutch, and remains so today. So, I believe that “rider”, the English cognate of the Dutch “ridder”, is the best gender-neutral term to mean knight or dame in the English language. I don't only believe this because it's gender-neutral in Dutch. It also has a history of gender-neutrality in English too.
In Old English, there were two words for this purpose: “cniht” and “ridda”. “Cniht” is the old word for knight, and “ridda” the old word for “rider”. Yes, the ‹k› in “knight” used to be pronounced. These two words were both, in a sense, interchangeable. And, they were both gender-neutral. Despite this, I think that fact can be overlooked. “Knight” has come to imply gender, while “rider” hasn't. The answer was almost hiding in plain sight.
English and Dutch aren't the only languages to have used cognates of “rider” as a gender-neutral term. Even today, many European languages use their cognates as a gender-neutral term. Other languages that do this are Czech, Danish, German, Estonian, Finnish, Scottish Gaelic, Norwegian, Polish, Russian, Swedish, and probably more.
The modern English word “rider” literally means someone who rides. I don't see this as much of an issue, because context can easily be used to avoid confusion. Besides, this is exactly what the old word meant. It's not that hard to imagine a knight, or rider, riding on a horse. If you look up “rider” on Wiktionary, it is even listed as an old or historical word meaning knight. The term is actually used in The Lord of the Rings as well. The second chapter of The Two Towers is titled The Riders of Rohan. These riders do, of course, literally ride horses, but the fact that rider is used for this purpose in such a popular work of literature is good enough for me.
What news from the North, Riders of Rohan?
In conclusion, it would be best to knight people using only one word, regardless of gender, but otherwise, “rider” is the best non-binary equivalent.