وَإِذَا سَمِعُوا اللَّغْوَ أَعْرَضُوا عَنْهُ وَقَالُوا لَنَا أَعْمَالُنَا وَلَكُمْ أَعْمَالُكُمْ سَلَامٌ عَلَيْكُمْ لَا نَبْتَغِي الْجَاهِلِينَ
And when they hear ill speech, they turn away from it and say, For us are our deeds, and for you are your deeds. Peace will be upon you;
we seek not the ignorant.
I do not think the Fatwa (in the link you provided) is helpful. It does not account for the situation nowadays and I think it does not take into account the circumstances in which Muhammad said those words.
Please refer to this discussion in which the circumstances are described. It makes sense. Think about it. Islam is peace and love, not otherwise. If a Muslim does not greet someone, then because he/she has a strong reason to do so. Merely being of another faith is not a strong reason.
Let me summarize:
- The Hadith must be read and understood in its context. It was in a time of hostilities.
- The mentioning of Christians could be due to fuzzy translation. The word Ahl-Al-Kitab is actually being used in Arabic; this can mean Jews and Christians, Christians or simply Jews.
- Some Jews were greeting with Death upon you which sounds similar to Peace upon you in Arabic. It is reasonable to believe that Muhammad simply did not want to stimulate this badness. So simply do not greet that person.
My sincere advice to you:
- Initiate the greeting to anyone in his/her language according the his/her cultural customs. In Arabic we greet in the usual form in Arabic; in English we do likewise in English, etc.
- The greeting in Arabic meaning I wish you peace is indeed a noble greeting; not many languages, nations, cultures have this privilege. Use it when you can, but don't exaggerate. Speak the local greeting.
- Don't stimulate bad behaviour. In this case refrain from greeting, but stay polite, keep your heart away from anger.
Abraham's (Ibrahim in Arabic) father was a polytheist.