We seem to know so much about the Anglo-Saxons in Britain, but very little about the early Frisians, Franks and Saxons in the post-Roman Low Countries.
To what extent can the much more extensive information about the Anglo-Saxons and other Germanic peoples in post-Roman Britain also be applied to the Germanic peoples in the Low Countries, about whom we apparently have much less information?
Did they worship the same gods? Did they eat the same food? Did they speak the same language?
Did they speak the same language?
Old English and Old Saxon were mutually intelligible, but are considered different languages.
From Genesis B, Old English:
Hu sculon wit nu libban oððe on þys lande wesan, gif her wind cymð, westan oððe eastan, suðan oððe norðan?
The same text from the Old Saxon version:
Hû sculun uuit nu libbian,|efto hû sculun uuit an thesum liahta uuesan, nu hier huuîlum uuind kumit|uuestan efto ôstan, sûðan efto norđan?
Both the Anglo-Saxons who came to Britain in the middle of the first millenium and the inhabitants of Frisia, the modern Netherlands and northern Germany spoke languages belonging to the West Germanic language subgroup. Mutual intelligibility between these would have been rather large, probably greater than the extent of later mutual intelligibility between the Ango-Saxons and the Vikings, whose Old Norse was in the North Germanic language subgroup, which had been split from continental Germanic for some hundred years, and who had not adopted Latin writing. Around 0CE, before the Anglo-Saxon migration, it is thought that all of the Germanic languages were no more than dialects of the same proposed proto-language. The ur-heimat of the Germanic people are placed for example by Nielsen (1998: 60) precisely in the North Sea coast region and up to Denmark based on linguistic evidence.
Geographic displacement, social make up, political factors and time separate this ursprache so as to make today's distinct languages, but at the time you ask about, separate development of Old English has arguably not gone far enough so as to exclude that it is basically placed in a dialect continuum with the languages of the continent.
Did they worship the same gods?
I suppose it depends. Do you see the Jewish, Muslim and Christian god concept as the same? The names for the pagan gods would've sounded similar, but if the one group expanded the function of, say, Wotan, to also include x, we don't know. Of course, rather rapidly, at least the Anglo-Saxons became Christians.