In this post, I will look at how it is possible for Finn and Fionna to meet.
Alvin and the Chipmunks
First off, lets look at the Chippettes. They are basically gender-swapped versions of the Chipmunks, yet they co-exist in the same universe with the Chipmunks (or, going by the newer movies, they LIVE together). If the Chipmunks and Chippettes can co-exist in the same universe without trying to kill each other to avoid duplicity, then I see no reason Finn and Fionna can't do the same thing (BTW, I reject Ice King's sick fanfiction and substitute my own).
Second off, lets look at Adventure Time's rival show "Regular Show". The characters Margaret and Eileen are also basically gender-swapped version of Mordecai and Rigby. But like the Chippettes, they co-exist in the same universe, and they clearly have feelings for each other, but they are one-sided for Mordecai and Eileen; Margaret is oblivious of Mordecai's feelings, while Rigby is aware of Eileen's feelings for him, but chooses not to acknowledge them (but it has been made clear they get along quite well, and I will be watching these two in the near future). Even if Margaret is a cardinal and not a blue jay, and Eileen is a mole and not a raccoon, the parallels between these two duos are clear. Using that logic, you can see that a meeting between Finn and Fionna is extremely possible, and logical.
In closing, with those pieces of evidence in mind, Finn and Fionna shouldn't seem so distant anymore. They CAN meet, in spite of what Pendleton Ward says. Perhaps someone should present this evidence to the Adventure Time staff. Thanks for reading.