To be honest, Islamic proselytising has always been a part of Islamic orthodoxy. However, you will need to divorce your understanding of the term when looking at Islam compared to when it is undertaken in a Christian context.
We give 'dawah' which is invitation to Islam and 'nasihah' which is advice in Islam. These can be done 'directly' or subtly with actions of great noblity, humility, understanding, brotherhood and charity.
When a person knocks on the door of conversion, we should hold them back, warn them of the hardships that will follow by becoming Muslim and that should ensure a healthy process of enlightenment.
We stress that conversion is done by Allah (SWT) and we are only agents who do the bidding and bring the 'message' to where it is needed. A Muslim should therefore be an embassador for Islam at every opportunity.
Rather than asking whether prosetylising is required by a given persuasion it would be easier to ask which factions to not require this, for sure this will be easier to determine.