Comparing polymorphic types in c++20

As an intermediate solution you could re-factor your polymorphic equality operator== to a non-virtual operator== defined in the base class, which polymorphically dispatches to a non-operator virtual member function:

struct Identifier {    
    bool operator==(const Identifier& other) const {
        return isEqual(other);
    }
private:
    virtual bool isEqual(const Identifier& other) const = 0;
};

// Note: do not derive this class further (less dyncasts may logically fail).
struct UserIdentifier final : public Identifier {
    int userId = 0;
private:
    virtual bool isEqual(const Identifier& other) const override {
        const UserIdentifier *otherUser = dynamic_cast<const UserIdentifier*>(&other);
        return otherUser && otherUser->userId == userId;
    }
};

// Note: do not derive this class further (less dyncasts may logically fail).
struct MachineIdentifier final : public Identifier {
    int machineId = 0;
private:
    virtual bool isEqual(const Identifier& other) const override {
        const MachineIdentifier *otherMachine = dynamic_cast<const MachineIdentifier*>(&other);
        return otherMachine && otherMachine->machineId == machineId;
    }
};

There will now no longer be an ambiguity as dispatch on the isEqual virtual member function will always be done on the left hand side argument to operator==.

const bool result = (user == machine);  // user.isEqual(machine);