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There are quite a lot of questions which touch on this issue, but there does not seem to be any that sets out any general principles for deciding when it would be a good idea (or a bad idea, or a pointless but non-harmful idea) to model a variable as both random and fixed.

There is a question which presently has a similar title, but which on further inspection is mostly focusing on one specific situation. There's another question which talks about the case of a binary variable, and in which the general impression from the comments seems to be that modelling the variable as random and fixed is always pointless.

user1205901 - Reinstate Monica
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    (+1) This is an interesting question, it comes up occasionally and is almost always very tricky.The only times I can see that it makes sense is when the factor is treated as a fixed effect and then also interacted with a random effect in the random structure. So the simplest situation would be `y ~ fixed.factor + (1|fixed.factor:random.factor)`. I don't think it ever makes sense to have `y ~ fixed.factor + (1|fixed.factor) + (1|random.factor)`and now I am trying to think of general sitatuation / general principles ! In the linked question which cites the Barr paper, I don't think it arises. – Robert Long Jul 08 '20 at 05:25
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    For the avoidance of doubt, this is about the situation where a fixed effect factor also appears as a grouping variable in the random structure (ie random intercepts) - not random slopes - right ? ? – Robert Long Jul 08 '20 at 05:28

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