If the driver is letting you through, then go through. "no victim, no foul", as they say.
Remember that you're not on the track for any other reason than to stretch your LFS legs and, optionally, get a qualifying position. You should be exiting the pit at a time that provides you the most clear track possible, and since you're not in the ongoing race, you can comfortably afford to drop back from any car ahead of you to create clear track. If it's not working, give yourself a drive-thru to get a different position on the track. Don't forget that the pitlane facilitates this kind of strategy.
Most importantly, though I know it sounds harsh, mid-race joiners don't have any rights on the track.. and if a mid-race joiner doesn't like the fact that they're stuck behind a slow car, and none of the above remedies or options are working, the only other thing I can recommend is to press Shift+S.