Should Christians learn Arabic?
Only if they think they absolutely have to.
In my previous life I was a linguist and a language/intel analyst. Throughout my life I have formally studied five languages, including Arabic, and I have informally studied several others. I have enough “credits” in Arabic that if they had all been earned in one school and one program, I would have a second BA (my first BA is in Russian). So I think I know whereof I speak.
Of all the languages I have studied, Arabic was by far and away the most difficult. Modern Standard Arabic (MSA) is nothing but a modernization of the language of the Qur’an. Its grammar is so convoluted that it makes a 10-acre corn maze look like Straight Street in Damascus (I’ve been there, and it is definitely straight). If you go into the Arabic world speaking MSA, you’ll get laughed at. Nobody speaks it, except on formal television news programs and the like. Each part of the 15 or 16 major parts of Arab world has its own dialect, and these differ so much that someone from the Magreb would not be understood by someone from the Levant or the Gulf. And the Muslim world east of the Persian Gulf doesn’t speak Arabic at all.
Someone who is really interested in communicating in the Arab world should start with one of the major dialects. I would recommend Egyptian. Most of the Arabic-language movies are made in Egypt, and that makes the Egyptian dialect understood throughout the MENA (Middle East - North Africa). If you go into the Arab world speaking the Egyptian dialect, you will likely be understood, even if you might not understand the person speaking to you.
That said, there are other languages that would be more useful for Western Christians to study, especially Latin American Spanish, for those living in the U.S.
As for Arabic being the language of peace, well,

is all I’m going to say about that.