From a survey of voters in the 2000 election, the estimated percentage of people they talk politics with who supported Bush for president:
Each respondent was asked to name up to four contacts. On average, each respondent discussed politics with 0.5 family members and 1.4 others. The two plots show separate estimates for the two groups. The top, middle, and bottom lines on each plot show the results for Gore and Bush voters in strongly Republican, battleground, and strongly Democratic states, respectively.
Unsurprisingly, Gore voters were much more likely to know Gore voters and the reverse for Bush voters. The differences between red, blue, and purple states are tiny among family members (about three-quarters of whom share the political affiliation of the survey respondent) but are larger for friends. On average, Bush voters perceived their non-family conversation partners to be more similar to themselves, compared to the perceptions of Gore voters.
(Thanks to Christian Logan for crunching the numbers from the National Election Study.)
The headline is somewhat misleading, in that it seems to equate "know" with "talk politics with". Alas, a good many civilized people refrain from talking politics with people whose views differ markedly from their own for fear that the resulting arguments will turn out to be more angry than illuminating. Thus we all tootle along in our solipsistic little universes, convinced that almost "everybody" thinks the way we do {g].