Well, I joined the Lodge in 1973. At that time there were members who had been members for 30, 40 and even 50 years, so that means that I knew some men that had become Masons in the 1920s. Now I can only speak for a very small area of the country (rural Northwest Louisiana), but there was never any effort made to conceal Masonic membership, in fact I would say it was more well know then than it is now. The Lodge Hall was the only 2 story building in the Village and was prominently marked and known to be a Masonic Lodge. There were many more Masons, Masonic Funerals were very common, corner stone laying ceremonies were much more common. Masons were generally held in high regard and many prominent citizens were Masons and known to be Masons. Open meetings were common where the public was invited. There were even events at Churches that we would attend as a group and wear aprons.
To offer a possible perspective on your meeting: You and this other man are introduced to each other and identified by him to both be Masons, but he himself is not a Mason, so in fact he does not actually know if either of you are Masons and is not able to "vouch" for the two of you being Masons, so the two of you do not actually know if the other person is in fact a Mason. Yet, you apparently shake his hand and give him a Masonic grip. So, he may have been put off that you would do that in public in front of a man you both know is not a Mason, and that if you had learned one of the lessons of the degrees you would not have done it. I suggest you think on what "lawful masonic information" means in respect to having Masonic communications with someone.
They may not do it in your Lodge, but at the degrees I have witnessed, at the end of the degree, someone instructs the candidate that the only people he knows to be a Mason are the men in the Lodge. Of course that number increases as you sit in Lodge with more members and/or introduced to other Masons by someone that you know to be a Mason.