That isn't a problem with Slack. That's a problem with the way people are using Slack. If the only workable fix is to use a different tool you have a far bigger problem at your company.
I can't fathom how anybody would have been able to work if they had gone as far as allowing notifications to be turned on and make noises at them every time Slack thought something Important Enough To Interrupt You had happened.
All the notifications and noises can be switched off, and the @channel and @here notifications can be ignored on a per channel basis.