I called Dining during a trip when an issue that might have kept us from making the reservation came up, and they told me that anyone showing up within 15 minutes of a reservation would be seated. That has been my experience, as well, as we do a ton of ADRs on every trip and have been late to a handful of them. We've never been turned away, even when showing up to Ohana 20 minutes late.
WDW ADRs don't really hold a table for you, unlike many real world restaurants. Instead, they give you a place at the front of the virtual line to wait for availability. That's why you often have to wait for your table even though you were on time or early for your reservation. So showing up a bit late doesn't cost WDW or the servers any money, as the same proportion of available tables are going to be filled regardless of exactly when you show.
WDW knows what transportation can be like to get around their massive resort, and the scheduling issues FP+ can cause. They also know that they themselves routinely make guests with ADRs wait 10-15 minutes or more to be seated at popular restaurants. It wouldn't look good for them to routinely require guests to wait, but on the flip side to deny entrance to a guest who showed up a few minutes late.
Unlike some of the more militant posters on Dis, WDW doesn't take a punitive stance toward families who might take a bit longer than anticipated to get to their ADR.