This is a very complex ideological question with a few assumptions.

Communism is indeed not a particularily homogenous political movement. Is hard core Communists people who believed in the Soviet union or Communists with no tolerance for reform politics? Or are they simply just people who dress in red clothes and go to special Communist parties in the forest (excuse my slight sarcasm ;) )?

Further more, reactions and different attitudes inside the Socialist and Communist movement differs greatly from nation to nation. Communists in West Germany probably had a more vivid reaction to the whole affair, while other western nations had a more distanced reaction. I would reckon reactions from Asia, China amongst others, would be greatly different and would be interesting to juxtapose against the west.

I have another question regarding the Berlin Wall. How long was the wall? I am aware of how well guarded it was which made it difficult to cross, but couldn't people have just traveled out of Berlin and went around the wall?

How did hard-core Communists deal with the fact that a huge wall had to be erected to stop people from running away from Communist rule into an evil Capitalistic state

Weren't there also many people who fled east?

I assume you're talking about people not actually within the Eastern bloc, but communists abroad.

Communists in Western Europe and Australia largely opposed the wall and denounced it in the same terms as non-communists. By the sixties, a sizeable majority of socialists outside the USSR had already denounced the USSR in one of three waves: the libertarian socialists had denounced it early on with the Leninist policies of New Economic Policy and War Communism, the democratic socialists had denounced it during the Stalin period (or during the immediate post-Secret Speech period when revelations about Stalin's activities became more known), and the Stalinists during the 'revisionist' Kruschev period. The 1960s was the period of the New Left in the USA and UK and the Whitlam administration in Australia, and there were few people still supporting and advocating for the USSR or the USSR's satellite states in the Eastern bloc.

But the people who remained loyal and tried to justify it are the ones you're probably thinking about. Their most common justifications were generally either

(A) the Berlin Wall is necessary as a national border, and to prevent espionage. You can see in this map that Berlin was an enclave deep within East Germany. These people generally said that the Berlin Wall and its checkpoints were a national border like any other, and were especially necessary because Berlin had become the world's hottest espionage zone, a relatively unpoliced border between two Cold War enemies

or

(B) The Berlin Wall is necessary to prevent publicly-produced or tax-subsidised goods produced in East Germany from being sold for profit in West Germany by profiteers.