The scientific knowledge is that which is produced based on a data set of quantitative or qualitative nature that are related to and analyzed by technical instruments, and produce reliable results based on evidence already produced scientifically. This knowledge requires the development of certain capabilities that enable understanding of the relationship between data. The knowledge that is the general public, is based on scientific knowledge, however this often builds on noted in the beliefs and attitudes that people in general have about a subject (empirical knowledge), because they do not master certain concepts and tools necessary to understand the said scientific Knowledge.

The short answer is no. Public knowledge and scientific knowledge is NOT the same. Hopefully, much of public knowledge gradually accept the scientific facts, but this is not a guaranteed case. Public knowledge is very much what the majority thinks, but Science is not democratic. For most of the really big scientific revolutions, the scientific "new thinking" have been rejected and ridiculed for years and sometimes decades by the public ... Examples: Layout of the solar system (Gallieo etc) was resisted by the church and probably the general public for decades if not centuries. 

What I consider a more critical problem is if the scientific community gets "frozen" into a fixed theory, which it is not allowed to challenge. Usually researchers can ignore public opinion, but if their peers rejects the idea (without checking it) bans it from the journals etc, it becomes very problematic. There is an interesting example of this: The treatment of Ulcer. In the 80'ies some Australian researchers suggested that it was a bacteria infection, which was however rejected by the entire community. Some years ago the researchers got the Nobel price, but it took a decade to this accepted. Nowadays, we can hence treat ulcer with antibiotics. 

In my opinion, it is hence very very important that Science is free: ANY QUESTION WHAT SO EVER CAN BE ASKED IN SCIENCE.  The moment we/the society tries to ban certain questions from scientific inquiry, we are on the road to a frozen science.

Though I do empathize with the opinions mentioned above, I tend to believe that the answer is really not that obvious. Could be that scientific knowledge and public knowledge are indeed not synonyms; however, it doesn’t mean they shouldn’t be. This is a highly controversial theme and lots of arguments can be brought into discussion. I wish not to be that categorical in saying YES or NO.

I agree with the example of Galileo… in those years the Church was the only authority to decide which theory was correct and which one was wrong (a heresy)… and in our modern times, aren´t the scientific societies kind of like doing the same thing?... it would be nice to discuss about it (how important the social setting becomes in this analysis, isn’t it?)… Scientific societies of any kind are definitely not exclusive clubs and should not be seen nor act as such either! They do not hold the ultimate truth (to be remembered that theories are always falsifiable in principle!)… so I do agree with the fact that a “critical problem is if the scientific community gets "frozen" into a fixed theory, which it is not allowed to challenge.”

But regarding the following statement… “The moment we/the society tries to ban certain questions from scientific inquiry, we are on the road to a frozen science”, I am not that sure of the real meaning of it or its implications… I do believe in the freedom of science; however, what happens when scientists propose to investigate topics which are too private for scientific study, or employ methods highly controversial in their testing?... where are the limits and who gets to establish them?

In the end, I feel it is important we remembered that theories are merely conjectures … and we always have the freedom to bring in new elements which contradict the existent theories and, thus, lead to the creation of new ones… but yes, then once again, and unfortunately, regardless of the period of time in which we live, we all do have this aspect in common: we always fear what we do not understand… or simply put otherwise, we always fear what seems to contradict our well-established beliefs…