What does 是 mean/indicate in sentences such as 虽然有些人吃素是因为宗教的关系，但小林不一样?
「是」因爲 translates to 「is」because of or 「is」due to. There's an implicit phrase that's omitted in these sentences, which is (the reason behind)...「is」due to....


  雖然有些人吃素「是」因爲宗教的關係，但小林不一樣。
  
  Even though (the reasons behind) some people eating vegetarian「is」due to religious considerations, 小林 is different.
  
  小林不太喜歡吃肉食，「是」因爲有些肉食有很多骨頭，讓他麻煩死了。
  
  (The reason for) 小林 disliking meat「is」because some meaty foods contain a lot of bones which greatly inconveniences him.


Like the English equivalent of these sentences, the phrase the reason behind is omitted. The English equivalent, however, will also omit「is」for grammatical reasons:


  Even though some people eat vegetarian due to religious considerations, 小林 is different. 小林 dislikes meat because some meaty foods contain a lot of bones which greatly inconveniences him.




Please note that in Chinese, the omission of the reason behind is necessary in this case; we don't say ...的原因是因爲..., especially in written materials, as this is highly redundant.