Since you mentioned that this happened in a baseball game...
There is a baseball interpretation that covers this play. If the batter-runner is in the process of taking the first initial step out of the box, and the catcher is in the process of taking the first initial step forward to field the ball...then the contact is ruled "incidental". It is neither interference or obstruction and the play continues without reference to the contact.
This applies when both players are "doing what they're supposed to be doing" and the contact is not deemed to be intentional. If either player is judged to have made intentional contact, then interference/obstruction can be ruled. Also, if the contact is made after one of the players pauses- say, if the batter-runner stood there a moment before exiting the box, then ran into the catcher after the catcher had already come forward- then obstruction/interference can be ruled.
Speaking softball...ASA used to have this interpretation in their umpire manual and high school softball had previously offered a similar ruling. Back a few years ago, when ASA re-wrote their umpire manual, the following section was dropped, so it's not there anymore. I have seen some debate as to whether or not it is still a valid interpretation. I would say that it is and would rule the play this way until told otherwise.
Here is what they had to say:
Simply because there is contact between the offensive and defensive players does not mean that obstruction or interference has occured. This is definitely NOT (emphasis their's) the case.
The field is laid out in such a manner that it, in itself, puts the offensive and defensive player on a collision course.
The right-handed batter, for instance, who lays down a bunt in front of the plate is on a collision course with the catcher when running in a direct line to first base. Each player at this point is within legal rights- the batter taking a direct line to first base and the catcher coming out from behind the plate to field the ball.
The questions that have to be answered are:
1) Did the batter alter direction in any way drawing contact, in an attempt to receive an obstruction call?
2) Did the catcher alter the attempt to field the ball in any way so as to draw the interference?
3) Could the catcher actually make an out on the play?
Again, this applies on a play directly in the vicinity of home plate where the players are crossing paths and the contact is unavoidable (which sounds like the type of play you are describing). After the batter-runner has exited the box is up the line, the same rules would apply that apply to any other batted ball. If the catcher is fielding the ball to make a play (ie: actually has an opportunity to make an out) the batter-runner is obligated not to interfere, wether intentionally or unintentionally. The reverse is also true- if the catcher is not in the act of fielding the ball or has no opportunity to make an out, then she is obligated to not obstruct the batter-runner.
