Gregory Huber and Neil Malhotra have a new research paper Political Sorting in Social Relationships: Evidence from an Online Dating Community (pdf). Here is one useful bit:
Relative to the average standard deviation by respondent for each outcome…shared ideology increases interest in responding by 12% of that amount, interest in long-term dating by 16%, and assessments of shared values by 20%. By the same comparison, shared lack of political interest increases assessments of likelihood of responding by a statistically significant 18%, but has more modest…effects on interest in long-term dating and assessments of shared values, respectively.
There is much more data in this paper, including a discussion of which issues matter to people the most. Here is one upshot:
…online dating pairings where communication takes place display greater political homogeneity than the population as a whole.