Not always. It depends on the degree to which it affects the individual.
A repeat history of (chronic) back pain, for example is an outright bar to entry.
If I was the OP, I'd consider renouncing dual nationality if I favoured military service in one country over another, but it's not for me to suggest it as it is the individual's choice. No-one else's, because there are both advantages and disadvantages to remaining dual nationality.