"pure islam" is an intriguing term, and is going to have two almost diametrically opposed meanings, depending on who is using it: it is either going to be a rallying cry for the most barbaric extremists you could imagine, or it's going to be an attempt for non-religious people with arab cultural backgrounds to essentially appropriate a jewish or christian identity as muslim.
the jewish scriptures are historically useless - which is to say that they aren't even necessarily wrong. this was such a long time ago, and the sources are so terrible, that you can't even prove them wrong, except through common sense. i don't need an argument to debunk the parting of the red sea. but, we'll never know whether or not there was a slave revolt, or whether or not people named moses or aaron had prominent roles in it. we can say that there appears to be archaeological continuity in the near east - that there isn't any sign of an invasion - but that's not really a proof that it didn't happen. good skeptics need to throw away the obvious nonsense and remain agnostic as to the general plot line. but, nonetheless, the jewish scriptures tell a story of a people that escaped from slavery with the help of divine intervention - and is then sent into slavery again, in repentance for their sins. a true judaism is consequently a kind of liberation theology. these are a people that identify as escaped slaves, and attach their ability to be free to upholding their pious behaviour: god gives them freedom in exchange for good behaviour.
the christian sources are only mildly better, but they hint at what is by far the most attractive society of the three. what we can piece together about these gnostic sects is that they were not much different than the mystery cults of the day - that they engaged in wild sexual practices under the influence of gratuitous drug and alcohol consumption deep in caves and other hidden places. a pure christianity is consequently a kind of pagan sex cult - but one that is built on egalitarian values and a crude understanding of socialism. then, power corrupts. remember: the office of the pope is actually the same thing as that of the high priest of rome. these conservative christian values only came in after the fact: christianity was initially pretty wild, and is on the very far left in it's most pure form.
but, islam doesn't have a history of this sort. mohammad was a warrior king, and these rules are designed to aid conquest. what islam is is a reflection of the christianity that existed in the period of heraclius. here's some history you don't know: jihad was invented by a roman emperor, who launched a holy war against the persians to recover the true cross and return it to jerusalem, then still a roman city. and, the crusades were more of a war against persia than a war against islam, the muslims merely taking the place of the iranians (and, the franks of the romans). pure islam is imperialism and colonization. it's ethnic nationalism. it's a set of rules to organize conquest with. and, it's a system of laws to decree in an empire, from the top down. this is inherently different.
so, the argument of "pure islam" comes from either direction. the truthful argument of pure islam attaches it to the ideology of isis, while the revisionist take tries to appropriate the christian heritage for itself, out of no legitimate history or actual tradition.
islam was more moderate in later stages. and, those seeking a moderate islam should be speaking of reformation, not of purity.
jagmeet singh must cut his beard.