What does 白沾 mean here?
沾便宜 is a variant of 佔便宜, in this case, »take unfair advantage of someone«. 
In that sense, 沾光 means »to bask in the light of someone«. 
I'd read 白 as »free« or »for nothing« here.
So the part of the sentence reads: 


  而我却不能给集体带来利益，这就等于是我白沾集体的光，丝毫没对集体予以回报。 
  So, if I can't give any advantage to the community, it means that I take its advantages for free, without giving anything back.