There is no connection to any claimed Mabille family or the recorded Mabe family.
Seargant Caspar Mabille etc. is long dismissed unproved data.
"Claes Janszen van Naerden" is recorded 26 Aug. 1636 age 33," so he was born ab. 1603(Van Rensselaer Bowier Manuscripts)
There are numerous individuals being "from Naerden/Naarden/Norden" and they are not related.
Claes Jansen is often recorded as "Ruijter/Ruyter"
He married Pietertse Jans
Claes was an Indian interpreter in 1645
his last recording is 16 June 1661 giving a report about his visit to the Esopus Indians (Documents relative to the colonial history of the state of New York p. 202)
Barbara Boram
vanboerum2@hotmail.com
Barbara Boram
This profile is 5 years old and the manager does not seem to have been active on Geni since 2011.
The connection between Claes and Caspar is popular, all 30 trees on MyHeritage all list the relationship, but popularity does not equal accuracy.
My immediate impression is that Claes' father name was Jan, anyone familiar with Dutch naming conventions would say the same.
I have editted the profile to set birth at c.1603 and death AFTER June,1661.
I have also added some of the name variations that you listed.
I have not disconnected him from Caspar and his wife nor any of his siblings as i am not knowledgable about early colonial America and do not want to create a larger mess than already exists :)
Perhaps someone more experienced in the area might suggest a way forward?
There are several web sources that show NO connections from Claes Janszen Ruyter to any Mabille/Mabe family, the "siblings" etc. show no documentation, much from myheritage is based on ancestry.com and there are many errors and most important no documentation at all.
I will soon update my Geni for Frederick Lubbertsen which will connect to Claes Janszen van Naerden/Ruijter. It would be correct to remove any undocumented data.