Betsy, there are many views on racing within the greyhound rescue fraternity. Obviously all the RGT branches are directly funded from the racing industry, so you will never see a RGT branch/website being critical of the racing industry. In fact they will usually defend it.
There is nothing intrinsically cruel about keeping a dog for racing, and many owners do treat their dogs well. Some aspects of racing life, the regular routines, co-housing with their fellow greys, healthy weight and exercise are arguably better than the life of an obese, lonely dog stuck in a house for eight hours by itself while owner out all day. I have met some very caring owners who are passionate about their dogs. However, there are intrinsic and structural issues that need to be considered.
Many campaigners would say that the racing industry is inherently problematic. A large number of dogs "disappear" (that is, shot/dumped) between puppyhood and racing, and then of course after racing. Dogs like ours are actually the tiny minority of lucky ones. There are a number of welfare issues associated with racing itself - in particular high speed cornering leading to leg breaks which almost invariably lead to being killed by vet rather than recovery (not cost effective).
To further complicate matters, here in Wales we have what are called "flapping" tracks - not under the control of GBGB. There are serious welfare issues - NO VET needed to be in attendance, for instance.
I think you also need to consider the fact that the majority of dogs raced in the UK are these days bred and raised as pups in ROI where again there are welfare issues (subsidised by Irish Govt). Irish Govt is seriously considering opening up overseas markets as the industry is in decline in the UK and ROI itself. Many greys end up in Pakistan and there are serious discussions about opening up racing in China. Unfortunately the welfare issues for greys in China and Pakistan are dreadful. There already has been one campaign to try to stop this development but the export of dogs to Pakistan continues. Life there for an ex racer is not a comfy retirement. Ironically, Pakistan culture doesn't "do" pet dogs (regarded as unclean)but they have a thriving dog fighting and dog racing culture. 
Structurally, it is impossible to consider the UK and Irish industries as two separate entities and the welfare issues need to be considered in the round too.
Hope this helps. Would be happy to point you to a variety of websites to give you further info.