يضمن (الدستور) حق الاعتراض أو الحق في الاعتراض

in legal writing objector is the one who is making or entitled to file or move for an objection, and objection is اعتراض

giving more context is highly required, just to allow more comprehension of the meaning of the article.

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Note added at 11 mins (2005-02-24 11:31:30 GMT)
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the conscentious objector is the person, who by reason of religious belief or training, is conscientioulsy opposed to participation in war. so the best translation of the term could be: ممتنع او معترض

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Note added at 20 mins (2005-02-24 11:40:43 GMT)
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i agree with مستنكف the conscentious objector is: مستنكف ضميريا the translation of the sentence could be: يحفظ حق الاستنكاف ضميريا

I agree that the literal meaning of objector is معترض. However, the meaning based on the process of conscientious objection seems closer to the meanings of إعراض or مخالفة. This is in the sense that the process relates to what the objector chooses for himself or herself vis-a-vis participation in an action (usually war).

الشخص الذي يدفعه ضميره أو تحفزه عقيدته الدينية أو الادبية الى عدم الاشتراك في الحرب والنفور منها

المعجم القانوني لحارث سليمان الفاروقي

one who refuses to serve in the military due to personal reasons of conscience

يعني أن أحقية الإحجام عن تأدية الخدمة العسكرية مكفولة بالقانون إذا برهن الجندي على أن تأديتها تعارض مبادئه الدينية أو الآخلاقية.
This is what I understand