What is the transgression? Persecution of innocent people. Attacking or invading another land. Attempting to wipe out a particular population or force them to convert. These are examples of transgressions.
Islam claims a false agression from non-Muslims particularly at the time of Mohammed. He is talking only to the believers (Muslims) and no one invaded during Mohammeds time so he is speaking about the pagans, Jews and Christians. Innocent is realative and it is Islam that wipes out and forced converts. It is unjust to say someone who resists Islam is transgressing Islam, but that is what the Koran says.
The cause of Allah, or the way of Allah, interesting question you asked. I’m not sure how to answer it, since I’m not sure of your mental frame.
Any context would be fine but one that tries to represent the many references in the Quran. Cause of Allah or Allahs Cause. A few examples.
Jihad (holy fighting in Allahs Cause) is ordained for you (Muslims) though you dislike it, and it may be that you dislike a thing which is good for you and that you like a thing which is bad for you. Allah knows but you do not know.
( سورة البقرة , Al-Baqara, Chapter #2, Verse #216)
And let not those among you who are blessed with graces and wealth swear not to give (any sort of help) to their kinsmen, Al-Masakeen (the poor), and those who left their homes for Allahs Cause. Let them pardon and forgive. Do you not love that Allah should forgive you? And Allah is Oft-Forgiving, Most Merciful.
( سورة النور , An-Noor, Chapter #24, Verse #22)
Those who spend their wealth in the Cause of Allah, and do not follow up their gifts with reminders of their generosity or with injury, their reward is with their Lord. On them shall be no fear, nor shall they grieve.
( سورة البقرة , Al-Baqara, Chapter #2, Verse #262)
Let those (believers) who sell the life of this world for the Hereafter fight in the Cause of Allah, and whoso fights in the Cause of Allah, and is killed or gets victory, We shall bestow on him a great reward.
( سورة النساء , An-Nisa, Chapter #4, Verse #74)