Do you suck at your religion?

[sasguru]

How is it an accident of birth when Asians are evangelised by Europeans to Christianity, or Europeans by Asians to Islam?

You're discussing religion as culture, rather than religion as a conscious personal decision; the two are very different and many religions say only one of those 'counts' properly.

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And what's your point? So a small minority of people are "evangelised" i.e. have their set of cultural, human artefact, religious beliefs replaced by those from another culture. Another random event, much like an accident of birth. It may be a more conscious decision - but it's not a particularly intelligent one.
A Muslim convert from Christianity has merely replaced one "holy" i.e. received wisdom book for another, one set of human cultural constructs for another.