Generally people call things rights even if they are technically privileges. People do that all the time with "right to drive" and others. Even rights can be taken away by the government. It seems that driving as it is treated now is consistent with other many rights when it comes to restrictions and removal of those rights/privileges. There's really no distinction necessary in the context of this discussion given that the function similarly.

"2) my claim was about the justification that people offer for their claimed rights, not the rights themselves."

The definition that you provided says nothing about justification being a part of something being extreme.

"Our collective decisions to keep driving today don't have the same effect on our psyches"

That's because driving is not extreme. It's considered a moderate position and people accept compromises on it. Even the people that say it's a right accept some level of restrictions such as traffic laws, at least from a standpoint of not wanting to be punished.

Simply wanting the freedom to move about by driving is not an extreme position.