Depending on how one defines their terms, some of the anticlerical violence in the Spanish Civil War could fit. But we would have to be very careful about our definitions. So let's start.

• The "last 2000 years" hurdle is an easy one, since the Spanish Civil War began in 1936.

• "Terrorist" is slightly more difficult. The violence against noncombatants in the Republican zone has been termed the "red terror" (as opposed to the "white terror" in the Nationalist zone), but that is a political definition (and a politicized term). The perpetrators would hardly have seen themselves as terrorists, as many were making a political point with their violence beyond trying to instill fear in their opposition. Repugnant as they were, the copious murders in the Spanish Civil War were largely targeted ones (though some of the targets were entirely fictitious, like the Nationalist execution of people they deemed "Jews" that were neither racially nor religiously Jewish).

• "Terrorist attacks" is an even more difficult term to apply to these cases, as the attacks on clergy don't comfortably fit the definition of a terrorist attack. The attacks on clergy happened almost exclusively in areas controlled by the Republicans and were ongoing for a number of months. They weren't done to influence policy in Nationalist Spain, but rather to eliminate perceived enemies. They were deliberately targeted at clergy, often individually. It is difficult to attach the label "terrorist attack" to these kinds of incidents, depending (again) on one's definitions.

• "Atheism" was certainly present amongst many of the culprits of anticlerical violence. The issue would come in with the "primarily motivated" part of that phrase. Few of the people who perpetrated these attacks left behind records of their motivations. Certainly some were vehemently hostile to the Catholic Church (as it is difficult not to assign malice when

People stuck cigarettes in the corpses' mouths and mocked the mummies. Some even performed impromptu dances with the withered corpses ... In the church of San Antonio de Florida in Madrid the mob played soccer with the patron saint's skull (The Spanish Civil War as a Religious Tragedy, Jose M. Sanchez, pg 44)

People's primary motivation would have to be sorted out on a case by case basis--and I have not seen a source that has done this kind of analysis. For now, I think we would have to not categorize anticlerical violence as "primarily motivated" by atheism. This is especially true due to the longstanding tradition of anticlericalism in Spain that is quite independent of atheism. Sanchez addresses that quite well in the aforementioned Tragedy, and he also points to other motivations. The Church was hardly pristine prior to the outbreak of hostilities, and both corruption and malfeasance on the part of a number of Church officials both high and low contributed to hostility towards Catholicism. As Sanches explains,

The anticlerical fury was a visible indictment of Catholic attempts to channel the essence of Christianity into narrow parochial ends. And worse, those Catholics who were not sacrificed to the fury condoned by their silence unchristian, inhuman reprisals against victims of circumstance, and they publicly lauded and supported a regime built in large part on oppression and special privilege. They became the clergy and laity of the church of vengeance, and they lost the opportunity to form the truly Christian church of reconciliation (199)

So to summarize, one would have to be extremely careful in defining one's terms. For the general use of the terms in question I would not personally say that the anticlerical violence of the Spanish Civil War would qualify as "terrorist attacks primarily motivated by atheism."

EDIT:

While I was writing my answer, OP posted the following:

I would consider atheism a primary motivation of a terrorist attack if the purpose was:

a) To destroy religion in the name of atheism b) To attract attention toward atheism so that it looks like it's fighting for the people c) To make people rebel toward religion

With those definitions, we might categorize the anticlerical violence in the affirmative. Reference Andrés Nin, who said "The working class has solved the problem of the Church very simply; it has not left a single one standing." (pg 46) I still wouldn't classify it as such, but with those terms defined much of the anticlerical violence in Spain during the Civil War would fit the bill.

this quickly breaks down into fun definitional games so op can you clarify a bit: what do you mean by an atheist ideology? how central does atheism have to play in the bombing's belief system for it to count? We can talk about stuff like the Vendee and the (Robespierre opposed) cult of reason but what about say anti religious actions taken by communists?

I doubt there were really any terrorists that were motivated to kill because they flew the "banner of atheism" but were there terrorist actions motivated by ideologies that were secular or atheistic? Yes, many. But, as others have pointed out, we have to be careful how we define our terms.

Someone here has mentioned the Spanish Civil War. I'm glad this was brought up (Ph.D grad student in modern Spanish history here). We have to be careful when we talk about the anticlerical violence example. Anticlericalism has a long history, not just in Spain, but in the rest of Europe. Anticlericalism was SOMETIMES motivated by a total hatred of religion, but more often than not, it tended to be directed mostly at Catholic hierarchy and institutions, and not necessarily at the theology itself. Most Spaniards tended to at least be nominally Catholic, and their frustrations with the Catholic Church were more material than theological. That being said, Spain has a long tradition of anticlerical violence, usually as a reaction to the increased influence the Catholic church may have had at a particular time period. Anticlericalism came from liberal, republican, and anarchist circles, and each faction varied in the extent of its hatred towards faith. Some (the anarchists) were ideologically atheistic, others merely politically angered at the catholic church's attempt to interfere with the establishment of a secular republic (Spain's second republic, 1931-1936).

Yes. I'd argue that the anarchist violence of the late 19th and early 20th centuries in Europe and North America could be considered atheistic. Take as an example the case of Luigi Galleani, an Italian anarchist who promoted the use of violence as a catalyst to overthrow government and non-government institutions.

In 1919, several followers of Galleani orchestrated a bombing campaign against authorities in U.S. cities. On June 2, 1919, bombs exploded at a Catholic church called Our Lady of Victory in Philadelphia. Other bombs exploded in different locations. Two bombers were killed attempting to deliver a bomb to the home of attorney general A. Mitchell Palmer. Others were supposed to be mailed to their targets but for various reasons never arrived.

Among Galleani's work was his time as the editor of Cronaca Sovversiva, (Subversive Chronicle), which was published in Vermont for 15 years until federal officials shut it down. Now, I don't speak Italian, so I have to rely on third-party translations.

The articles in Galleani's newsletter included such things as arguments for free love and against the existence of God. Galleani and other anarchists ─ particularly in Europe ─ saw the Catholic Church and other organized churches as instruments of the state. Catholic churches and officials were attacked via bombings and assassination attempts, particularly in places like Spain, Italy, Boston and New York City.