Friendship with only one topic

Solution 1:

In U.S. English, it's common to refer to people with whom you have a positive relationship based on a single shared activity by the name of that activity followed by friend or friends. For example:

• He's a volleyball friend.

• She's a birdwatching friend.

• They're writing-group friends.

• We're drinking buddies.

I don't think that a widely adopted generic term for such friendships exists. None of the possibilities that come to my mind—"single-connection friends," "one-activity friends," "shared-interest friends," "context-dependent friends," "facet friends"—seems especially appealing.

Solution 2:

May not be the exact answer, but I simply think of something that I never heard before, "topical friendship". And I've found something, that in my view, support the idea.

There’s nothing wrong with Carole or Tanya for maintaining this mostly topical friendship that only occurs when they happen to see each other. Just think about how often a grocery store cashier asks, “How are you?” before s/he starts ringing up your purchase. Your response is probably an automatic “Fine.” I’ll bet you don’t dump your family drama, a recent health scare and financial troubles on the conveyor belt along with cantaloupe and dish detergent.

Update:

Inspiring with @Edwin's comment and based on the page 470 of "The Global Internet Economy", it seems that Homophily could fit the situation that OP describes. In Wikipedia it is defined as:

Homophily (i.e., "love of the same") is the tendency of individuals to associate and bond with similar others. The presence of homophily has been discovered in a vast array of network studies. More than 100 studies that have observed homophily in some form or another and they establish that similarity breeds connection.These include age, gender, class, and organizational role.