@ Steve, I agree with your observations and considerations. And yes, the remaining question is: do we have the right Frederik Idesen baptized in 1675 or does J.P.?

Can we tie Ide Frederiksen, his wife Lijsbeth Jans and/or some of their children Grietje, Annetjen, Anna, Jan or Lijsbet Idesen to the family in Spaarndam? Or can we tie Antje Cornelis de Git or Maartje Claas to Grietje, Annetjen, Anna, Jan or Lijsbet Idesen?

As to Maartje Claas from Alkmaar I can find dozens of candidates Maartje, Maritje, Marijtje baptized in Alkmaar in about the right period who have a Claas as a father. 

etc. etc.

But more important is what is written about Maartje with the 1707 marriage: "Maartje Claas J. D. van Alkmaar, wonende onder de banne van Velsen." So she was not living in Haarlem or Spaarnwoude or Spaarndam prior to the 1707 marriage. And not born in Spaarndam or close surroundings.

Hence the candidates in the Spaarndam registers do seem irrelevant to me. But the general approach to find the baptism of a Maartje in about the proper period - but in Alkmaar - who does have siblings that appear later on as witnesses (Grietje CLAAS, Trijn(tje) CLAAS) is imho the right one. Which may then be narrowed down (since I expect multiple possibilities with these common names in a big town like Alkmaar) by looking for a connection to Velsen. But literally to begin with a bit of a needle in a haystack. Distance Spaarndam - Alkmaar is I guess around 35 kilometers:

@Bart:  Concerning Maartje Claas, I think at this point, the only candidates remotely close to the family structure are these:

Dopen (Grote Kerk)
Bron: doop-, trouw- en begraafregisterSoort registratie: doopakte(Akte)datum: 16-06-1683
Plaats: Alkmaar
Dopeling: Grietje
Vader: Claes Jansz
Moeder: Maertje Jans

Bron: doop-, trouw- en begraafregisterSoort registratie: doopakte(Akte)datum: 03-11-1689
Plaats: Alkmaar
Dopeling: Maertje
Vader: Claes Jansz
Moeder: Maertje Jans

By no means, am I suggesting I have resolved the matter.  So far, I am having difficulty locating any Trijn(tje) to a Claas or Claes.

Could be.... 'Trijntje' could be short for 'Catharina'. On the other hand, I have found a couple Claas Jacobusz X Aafje Claas with daughters Catharina (Trijntje) and Margaretha (Grietje). Among other children, but have not found a Maritje/ Maartje. Aafje, because of Frederik X Maartje's eldest daughter. Unfortunately a dead end for now.

@Bart: an interesting find, especially the mother's name. Definitely not conclusive but intriguing nonetheless.

For now, we can now know Maritje was from Alkmaar and concerning Frederik, I'm more inclined to go with Medemblik as his birthplace. 

We gained a little more knowledge about Frederik than I did before posting my inquiry.  That he was married twice, with offspring from both marriages.

I'm inclined to agree that Frederik's origins are Frisian. Just a suspicion.

Just wanted to take a few moments to thank contributors to this discussion item.  Unfortunately, I have been unsuccessful in resolving the question of Frederik and his wife's parentage.  The good news is at least I learned that Frederik was married twice, with children by each spouse, marriage date and place, and their place of origin. All in all, it has been fruitful and is deeply appreciated by me.