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Bride kidnapping, in general, is specific to the Kazakh community. It's not what Western communities would imagine of kidnapping, in that the woman's family is often aware of it happening and indeed (and terribly) their knowledge of it is used to help pressure the woman into agreeing via social isolation and exclusion. It's largely ritualized and does not involve random people off the street:
In the case of non-consensual bride kidnapping, a woman is physically kidnapped by a man she hardly knows or by a man she is clearly not interested in.
As such you and your travelling companions shouldn't be targets for bride kidnapping.
However there are anecdotes about foreigner abduction and ransom in Mongolia, despite official figures to the contrary. That would be of more concern, but it seems that occurrences are no more likely in the Kazakh parts of Mongolia as opposed to any other part of the country, or indeed other countries.