这个句法现象叫 delayed right constituent coordination。即两个结构并列时，因为右端有相同的成分，因而省略了前一个成分。这是语言简洁性的体现。

具体到这句里，实际上并列的是 spills over into religious beliefs and other customs 和 is often reinforced by religious beliefs and other customs 这两个动词短语，其中 into 和 by 的介词宾语相同，因而前者的被省略。

翻译：饮食习惯影响了宗教信仰和其他习俗，同时又（反过来）被这些信仰习俗所强化。

（上面括号里的字是补充性的意译，不是直译。）

再补充一些来自 CaGEL 的这种语法现象的例句：

- She knew of but never mentioned my other work.

- I'm interested in but rather apprehensive about their new proposal.

- He ought to, but probably won't, make a public apology.

- She was then, is now, and always will be, devoted to the cause of peace.

当然，就我个人而言，接触这种现象最多的情况，其实是各种协议条款里的 including but not limited to（包括但不限于）……