We use "take it for granted" when we don't really have a conscious appreciation of something that we always expect to have or be able to use. Most people take it for granted that they have water every day. Some people are more appreciative of water and other basic necessities that many of us take for granted.
I'm not sure about "take it as read that" as a particular expression. To me, it's a phrase, but I can't say I recognize it as a kind of idiomatic expression in the same way that "take something for granted" is an idiomatic expression. I would say "take it as read that" means "take it as understood in general", but it depends on how it would or could be used in context.
By the way, it's important to understand other ways in which "grant" can be used.
Granted that ... - understood (in a certain way) -used to set up what someone is about to say
A grant from the government or a private organization for some sort of research, charity work, or artistic endeavor.
I'll grant you this ... I'll give you credit for this
I'll grant you this much ...
I'd look these up in Google or go to the HyperDictionary to check out "grant" and "granted". I have to warn you, though, that the HyperDictionary is too much. It can give one a headache.
Definition of GRANT (Meaning of GRANT), a 5 Letter Word
I would just read the part that is the definition. The rest could give you a headache.
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