Can I use the word "strand" to mean a "sort" of a "kind" of something,
Multiple books of all strands have been written on the issue?
If not, what would be a good alternative?
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One could argue that it would be understood but it may not be accepted since it's not idiomatic.
If you want to be more specific, then be more specific. Don't just make up a term and expect it to imply what you're trying to say.
Multiple books with differing opinions, motivations, and ideologies have been written on the issue.
The ODO defines the noun strand as "An element that forms part of a complex whole." definition 1.2 of the noun.
This is an extension of the meaning of 1.0: "A single thin length of something such as thread, fiber, or wire, especially as twisted together with others [my emphasis]."
So if I go outside and yank some grass up, I'm likely to end up with not only grass but maybe some weed(s), and/or a flower. So, in a limited manner, I'll have plants of all strands in my hand. And although I will also gave plants of all types/kinds, the meaning is not the same.
Strands are part of a complex whole (1.2). Types and kinds do not have this meaning.
Synonyms for strand include:
element, component, factor, ingredient, aspect, feature, strain
There are example sentences with strand in the ODO and other dictionaries that you can look at and learn from. After examining these sentences and you feel that your original sentence works, then go for it.
You could perhaps also say something such as:
Multiple books by authors of all strands (or: every strand) of thought have been written on the issue.
People come from all strands of life, and often authors write from all strands of thought. In this sense, they are each a part of the complex whole.
And even though people of all kinds probably include people of all strands, the two terms are not the same. This answer has attempted to show why.
If this is not what you want, you probably want to go with one of the synonyms for types that other answers have listed.
"Strand" might be possible here but I don't think it would be usual or the best choice. There are many possible alternatives. "Types" or "kinds" are the ones I would use. There are probably better alternatives. I would also consider changing "multiple" to "many" "a great many" "a huge number" or something similar.