There are two reasons supersonic jet noise will be allowed: people's willingness to put up with things that are new technology, and their apathy. People will allow things that bother them to happen if they feel there is a significant benefit. Even if that benefit is one that are not able to currently use, they will hope to benefit from it in the future. Also, the people who are bothered would have to make a significant investment in fighting it, and most people won't do that.
Since the days of the Concord, great strides have taken place to reduce the noise level of a sonic boom. Much like other noises in today's society, eventually people will become accustom to the sound as they have with the sound of a lawn mower or other such things. No matter what, there will always be people that complain. What I think is silly are the people who move next to an airport or train station so they are close to transportation then complain about the noise levels.
People will detest the boom. This is because technology has become more annoying than not. With cell phone and computers already taking our attention away from being civil to each other, sonic booms will just further show we are becoming less civilized and courteaous to one another as time goes on.
Supersonic travel, whilst it sounds a worthy goal, comes at a cost; noise pollution caused by supersonic jets breaking the speed of sound (the sonic boom). At a time when airline industry mega trends are based on reducing weight, reducing noise and improving fuel efficiency, the concept of supersonic jets is anachronistic and self-indulgent for the few who could afford to get there a bit quicker at the expense of the eardrums of the many.
I think if it will be as loud as some people say it will be then no, we will no accept this. Because of International flights, this noise could be happening constantly throughout the day and no one would be safe from it. I think it could be bad enough to scary people and cause accidents.