This claim is true. According to a story written by the UN Environmental Programme (UNEP), "Plastic fibres are polluting the oceans, the wastewater, toxic dyes, and the exploitation of underpaid workers. Fast fashion is big business, and while the environmental costs are rising, experts say there is another way: a circular economy for textiles." I also know just from looking at the materials of fast fashion products that they are usually made of polyester or a polyester blend, which is a plastic. There is also a statistic from Business insider, via Earth.org, "fashion production comprises 10% of total global carbon emissions, as much as the emissions generated by the European Union." Earth.org also supports the claim about the excessive amount of water that is used. They claim "The fashion industry is the second-largest consumer of water among industries, requiring about 700 gallons to produce one cotton shirt and 2,000 gallons of water to produce a pair of jeans."
Sources:
https://earth.org/fast-fashions-detrimental-effect-on-the-environment/
https://www.unep.org/news-and-stories/story/environmental-costs-fast-fashion