The only two border crossings where I saw a height problem were coming back into Stewart B.C. after being in Hyder AK for the day. I didn't want to go under the canopy so went to the left of it. Border guard said he really didn't want to do the paperwork for someone hitting the canopy, and the other was going into Alaska on the Alaska Highway. A fifth wheel went to the left lane and wouldn't fit under the canopy. The Border Guards had the three of us behind him back up and go through the open lane on the right, so they could get him backed up to go to the right as well.
The truck and camper are 12'6" tall . If you are aware of your size and approach the crossing slowly you will be able to take the uncovered lane.
We saw many Class A on the roads up there and I will second the protect your Jeep from rocks statement.