While I agree with others and especially
@Rdffigueira , I think that the absence of a First Crusade would imply, rather than cause, significant changes.
The safest bet, if we'd search a PoD to prevent the First Crusade to happen, would have been to override the evolution of the Xth century.
Crusades were possible thanks to a social/ideological evolution and integration of
miles* into a Christian way-of-life : If violence against Christians from a class whom whole legitimacy was based on warfare was frowned upon, the logical outcome for milites, in order to be religiously legitimized, was to use this violence to serve Christians.
Legitimisation of violence, especially from a military-based social class (less nobility as a whole strictly speaking than milites, aka warring nobility), that was in the direct continuation of Truce of God and XIth councils played an important role : it did help that Urban II was issued from this nobility, and most able to speak to them, calling to their own conceptions.
As armed protection of pilgrimage, partially-religious led expeditions were already a thing, if Byzzies wouldn't have asked for reinforcement, eventually a religious expedition similar to Crusades would have been launched with the whole base being present.
Eventually, what you would need is a weakened papacy before the XIth century, maybe no HRE in order to butterfly away the Ottonian Reforms, making Rome unable to really support movements as Peace of God or at least having them remaining under local religious control, and therefore and while more or less respected, not really susceptible to gather as much support or being abl to bypass as much imperial and royal authority to adress to directly to
miles as it happened IOTL.
It wouldn't butterfly away religious expeditions, would it be only because they already existed by then (in Spain, with participation of southern France's lords and Normans; in Italy with the lot of Normans and north-western French; etc.), but it would remain a more regional concern, maybe some on behalf of Byzantines (I'm not sure you'd have both ideological motivation and general structuration to launch autonomous expeditions, tough) and maybe Baltics. All with a more important secular drive.
It would have important consequences on political conceptions in Western Europe : overall, XIth Europe would be a relatively different place to live with less restriction on war and more direct nobiliar power or influence on regional clergy.
That being said, it's mostly implied rather than caused by the absence of Crusade : the direct impact on Latin Christiendom would be limited : Most of cultural transmission were happening in Spain or Sicily IOTL; Mediterranean Sea was already pretty much dominated by Latin and Greek navies in the late Xth; etc.
On Middle-East, Byzantines could have it a bit harder, but the truly chaotic situation regionally at this point would prevent a complete Turk takeover, especially with Fatimids being unopposed in southern Syria.
That said, Constantinople could maybe meet an earlier end, being more under pressure from Normans and not beneficing from as much Anatolia they had IOTL, altough I think Kommenoi could take back 1/3 of it with their own means.
*Roughly, miles are identifiable to knights, as a the lower step of medieval nobility up to the XIIth century, servicing lords or princes trough military service, some of them being landed.