You are confusing the things. Not eating meat has nothing to do with rat eating meat or some animals and nature being shown respect. Btw, people might not eat meat because they or their ancestors initially considered life (human or animal) sacred.  

Hinduism and Judaism are very ancient religions and include customs etc. from long ago. If you look at the Vedas, Puranas and books in the Old Testament, you will come across many strange things and practices mentioned there. All such incidents indicate the situations involving humans in relation to nature (including other animals) etc. during early civilization.

Thus when the civilization was developing, as indicated in various above texts, humans noticed that some creatures could consume or do things which they themselves couldn’t do. They considered these particular life forms,  capable of surviving on bad things and in inhospitable environment or endangering the life of people, as special. Similarly, animals and other things in nature (trees, rivers and mountains etc.) which benefited humans were also considered special.  Needless to say, all these special creatures and things in nature were accorded respect by humans, even in the form of worship which continues to this day as a tradition.

On the other hand, later religions -- Christianity, Islam, Buddhism etc. (which came out of Judaism or Hinduism much afterwards) – excluded such early civilization practices and worships (involving nature and animals etc.) from their dogma and literatures because they were not significant anymore. Thus you don’t see such practices in later religions. Hinduism has more of them because it’s the oldest religion. Btw, as indicated above, all these things and animals getting respect from people are not treated or considered equal to God. 

- Seva