Individuals identified by DNA testing as closer than the fourth cousin range haven't responded when I email to say hello. People who are identified as more distantly related have all responded, some quite enthusiastically maintaining contact. Perhaps when the genetic relationship is known to be closer, people fear that they'll feel a sense of claustrophobic obligation.
In a way, this is consistent with something I felt historically about some second cousins and most third cousins, I felt they were family, but I didn't have an interest in really connecting with them. I preferred my large first cousin family and, at the second cousin level, cousins who were multiply related to me. But I also felt that I was supposed to treat the more distant cousins like family, even though I didn't really feel a sense of emotional kinship.
On the other hand, encountering people who are 4th cousin or even more distantly related seems more like a fun coincidence unburdened by a sense of familial obligation.