I think it would take a lot for people to stop flying because of gas prices for two reasons.
Number 1, cost of gas is probably the smallest expense of aircraft ownership. Let's take the average 50 hours per year private pilot. What's the difference between $5/gal vs. $8/gal... Maybe $1,500 extra? That's nothing compared to the cost of annuals, hangar space, upgrades, maintenance, etc. I'm paying nearly $6,000 per year for hangar space alone. Before I quit flying, I would probably try to find a cheaper hangar solution first, if I'd really have to recoup the $1,500 I'm paying extra for gas.
Number 2, income. This may not apply to all of us, but I would bet it applies to most of us here on the forum. Spending an extra $1,500 a year on something we very much enjoy isn't going to break the bank. Most of us could shake loose that budget from other hobbies we enjoy less, or put in 10 extra hours of work this year and make up for it. I would also argue that overall (again, doesn't apply to everyone, but I'm almost certain to most of us), we have more disposal income today than we did 5 or 10 years ago. When I started flying a few years ago, I probably couldn't really afford it but in those three years, I more than doubled my income (I would say, partially motivated by my new flying hobby) while cost of living did not double... Sure, it went up, but not 2X.
Yeah and I try to apply this thinking to both auto fuel and flying instead of worrying. However, I think for a lot of us got to or maintain a financial position that will support owning an airplane by developing the habit of monitoring our spending and trying to be thrifty. Seeing such a proportionally large proportional increase in prices is... anxiety inducing.