Things are relative, i.e. I don't know if there have been more protests in Greece per capita than in France against such measures, but one element that is probably relevant is that unlike Italy where the Catholic church came out in favor of vaccines, even with stuff like
The Vatican has declared that it is morally acceptable for Catholics to receive COVID-19 vaccines, including those based on research that used cells derived from aborted fetuses.
Greece resembles its Balkan neighbors much more in this regard, in the sense that significant elements of the Greek Ortodox church have apparently been rather unsupportive or even opposed:
Τhe church leadership officially supports vaccination. The head of the Greek Orthodox Church, Archbishop Ieronymos, spent several days in intensive care with coronavirus last November. A month later, he said: "I would be the first to go and get vaccinated if I had not been sick." The archbishop announced he had received the vaccine on May 12.
However, several influential archbishops and clerics repeatedly tell the flock not to get vaccinated, while some refuse to let people into church if they are wearing a mask or have had the jab.
Seraphim of Kythira, one of the country's most powerful clerics, is even spreading the conspiracy theory that "vaccines are a product of abortions.”
"This product that comes from killed embryos will be injected into our bodies. ... They want to create a metahuman, a mutated man, a man who will be like a robot," he said. [...]
Rules that applied to everyone else, like wearing a mask or keeping safe distances, were never really applied in churches. Even a directive to hold Easter services earlier than the usual midnight, because of a nationwide curfew, was disobeyed.
In the region of Aitoloakarnania in western Greece, the top local cleric (known as a metropolitan), Kosmas, has called those who are afraid to attend a packed church unfaithful.
“God does not allow you to be infected. God does not infect! It is a holy place, the temple is heavenly,” he said. [...]
Early in the pandemic, the Holy Synod ruled that the virus cannot be transmitted through Holy Communion. Several priests who used disposable spoons for Holy Communion to avoid transmission of the virus through saliva were suspended.
By the way, vaccination against Covid in Greece is somewhat below EU average, but above Slovakia or Croatia, and well above Romania or Bulgaria, which are far behind.
Greece's current vaccination rate more or less matches what was predicted in surveys last year regarding vaccine hesitancy in the country, i.e. slightly less than 60% were willing.
According to the https://covidbehaviors.org/ running survey, Greece is well-above average in terms of how many respondents express concerns about vaccine safety. This jibes rather well with pre-pandemic surveys that identified lack of trust in pharmaceutical companies and lack of trust in government institutions as reasons for hesitancy in Greece, even among healthcare workers.