ok, sir, let's give you a
wikipedia answer:
so, christians take 33.06%, muslims 20.28%, for a total of 53.34%. that makes up for more than one half of the total count. so is there, in any way, that the remaining 46.66% be greater than 53.34%? sir, no matter what calculator i use, 46.66 - 53.34 always gives a negative answer. and sir,
in elementary mathematics, having a negative answer means that the minuend is less than the subtrahend (in plain english, 46.66 is less than 53.44).
let's take into account the non-religious and atheists, subtracting 11.92% and 2.35% from 46.66%, giving us 32.39%. so sir, is there in any way that 32.39% becomes a basis for something major, in comparison to 53.34%?
your premise, "major religions do not reject reincarnation", sir, is incorrect. you would be correct if, and only if, you would be saying that, "there are more religions believing in reincarnation".
as for the sources sir, that ISLAM and CHRISTIANITY reject reincarnation, you can read Roman Catholic Archives sir, and you will see that no OFFICIAL RC doctrine promotes reincarnation. the same goes for ISLAM.
sir, you believe that many religions believe in reincarnation. then, let us give the FIVE major religions.
[1]Christianity - no doctrine of reincarnation - How about the Nazarenes, the Christian Universalists and GNOSTICISM

[2]Islam - no doctrine of reincarnation - How about SUFISM

[3]Hinduism - believes in reincarnation
[4]Chinese Folk Religion - no doctrine of reincarnation - ARE YOU sure? how about TAOISM?

[5] Buddhism - believes in reincarnation
although, again, read at your own risk.