Two conditionals affirming the same consequent do not by themselves make their antecedents incompatible.
For example:
If Zayd is a student, he is human.
If Zayd is a teacher, he is human.
These statements do not imply that a student cannot be a teacher. A person can be both. A negative separation requires the appropriate contrast—affirmation on one side and denial on the other—in the same relevant respect.
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Conjunctive Syllogisms with Conditional Propositions
Two conditionals affirming the same consequent do not by themselves make their antecedents incompatible.
For example:
If Zayd is a student, he is human.
If Zayd is a teacher, he is human.
These statements do not imply that a student cannot be a teacher. A person can be both. A negative separation requires the appropriate contrast—affirmation on one side and denial on the other—in the same relevant respect.