At our field, both teams exit out of the same end of the stadium, and walk a path to the locker rooms. Officials will hold the visitors, and let the home team leave first. A couple of officials will walk up the path with the teams to the point where they separate. Thankfully, we have never had a problem. In fact, in many cases, the slow guys our our team wind up intermingling with the first guys on the visitors and they wind up talking to each other.
Coming back, they reverse the process. The officials come to the locker room to get us for the second half. If one team is on the path, they hold the the other one until the first one passes. It once caused us to be late to the field, but the officials with us told the R, and it was no big deal.
Of course, coming back, it's never an issue for me. Kickers come back early to warm up ahead of everyone else. Our biggest problem are the schools with big bands!