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Looks like you are using vuetify
so this should be possible. You can use slots to customize certain colums. This could be like this in your case:
<v-data-table
:headers="headers"
:items="politicians"
:search="search"
>
<template v-slot:item.party="{item}" :class="functionWhichSetsClass(item.party)">
{{functionWhichShowsIcon(item.party)}}
</template>
</v-data-table>
In this example you only customize the column for party
. So you can change the additional content and how it looks.
Source:stackexchange.com