Is public safety a sound reason for limiting constitutional right? Why or why not?

Yes it is to a degree. If there is a credible threat that is completely believed to be real and to investigate it more they have to breach someone's rights, I would say it is sound. Imagine if it was a bomb threat in some highly populated area. If the bomb goes off than hundreds might die. If they have to breach someone's rights to find it, I think it is acceptable.