Honestly this question is too broad. It's hard to tell what Erdogan's position was on each and every purge, because the (Western) media hasn't reported much on his views on the matter.
So, I'll just to try to address this
Is there reason to believe that this purge about getting rid of the Kemalist secular influence in the country and/or the government?
If we believe EU intelligence officials, many of the coup plotters were not Gullenists but Kemalists/secularists. So by extension, many of those purged in relation to that, at least in the army, probably had similar views.
A secret report written by Intcen - the EU’s intelligence agency - found that the hastily organised attempt to overthrow Mr Erdogan last year was motivated by the fact that military generals feared they were going to be subject to an imminent crackdown on the opposition.
“The decision to launch the coup resulted from the fears of an incoming purge,” the August 2016 report, seen by The Times, read. “The coup was just a catalyst for the crackdown prepared in advance.”
Before the coup, several factions within Turkey’s army were unhappy with the government’s attempts between 2013 - 2015 to make peace with the PKK, the militant Kurdish separatist movement, and Mr Erdogan’s interventionist stance on the conflict in neighbouring Syria.
Rumours of an expected purge joined army followers of the exiled cleric Fetullah Gulen, secularists, and those opposed to Mr Erdogan’s policies against the Kurds together, providing the momentum for the dramatic failed July 15 takeover.
European intelligence officials also found that the Turkish government’s claim that Fethullah Gulen - whom the country is trying to extradite from the US - was behind the plot were unsubstantiated.
“It is unlikely Gulen really had the abilities and capacities to take such steps... The Gülen movement is very disconnected and somewhat distant from the secular opposition and Turkish army,” the report said.
Also some detailes emerged on the original plotters:
Transcripts of WhatsApp messages among the coup plotters that fateful night reveal that the putschist group in Istanbul called itself “Yurtta Sulh” in a reference to a well-known maxim by Turkey’s founding father, Mustafa Kemal Ataturk, that goes, “Yurtta sulh, cihanda sulh” (peace at home, peace in the world). The choice suggests that there could have been a mix of disgruntled Gulenists, Kemalists, and ultranationalist soldiers among the plotters. As for the smoking gun — an order coming from Gulen’s Poconos headquarters — we haven’t seen that as yet.
The purge also disproportionately hit officers who were stationed in other NATO countries
Overall, more than 700 officers out of 950 officers serving at Nato and in Turkish diplomatic missions around the world are estimated to have been purged. Most have applied for asylum in their host countries, and some - in Germany and Norway, for example - have already received it.
and DW reported that NATO had not seen evidence any of their Turkish staff were involved in the plot:
the Supreme Allied Commander Europe (SACEUR) admitted to a small group of journalists, this reporter included, that he didn't suspect any of the 150 officers purged from allied military operations - halving the number of Turkish staff - had been involved in the overthrow attempt. On the contrary, the general explained, "I had talented, capable people here and I'm taking a degradation on my staff for the skill, the expertise and the work that they produced."
So the purge probably had more to do with whom Erdogan (and his party) mistrusts rather than a single opposing entity.
There are some personal accounts from the dismissed officers along those lines, e.g.
An interview with an unnamed Turkish officer in the Brussels-based Vocal Europe magazine provides a profile of the type of military personnel the country has lost. “I went through officer training in Turkey and abroad.… I got my master’s degree in United States. Like many other purged officers, I am a staff officer, graduated from War College,” said the military official, who currently runs the Twitter account @PurgedNATO. “Personally, I do not know why I was sacked.… I have extensive education in US, I probably did not fit well in the new Eurasianist clique, dominating the Turkish Armed Forces.”
“Eurasianist clique” is not a familiar term outside Turkish military circles, but it’s not a new one. An April 2003 cable, released by WikiLeaks, from the U.S. Embassy in Ankara describes the Eurasianists as a group of officers within the Turkish military “who, without understanding the Russia-dominated nature of the ‘Eurasia’ concept, have long sought an alternative to the U.S. and are considering closer relations with Russia.” The cable went on to detail how a rival group dubbed the “Atlanticists” — who believe Turkey’s strategic interests lie in its U.S. and NATO ties — was losing influence within the Turkish General Staff.
It's much harder to tell what sympathies had those purged in later rounds... Especially after the EU-Turkey migration deal, criticism of Turkey's purges/arrests has been less pronounced... unless it touched Western citizens (Germans in particular).
But regarding the Turkish academia, the picture is generally clear:
The educational sector has long been a target, especially because of its emphasis on the values of enlightenment and science, once adopted from the West. In his effort to raise “pious generations,” he [Erdogan] has had the teaching of Charles Darwin removed from national curriculum. He has called on parents not to send their kids to the West for education, lest they become “their agents.” (One should ask, of course, why he sent his own children to American universities: to avoid the whims of the previous prevailing “national and local values.”)