How is the process of creating PVC fabrics harmful for the environment?
I wouldn't think that the process of producing PVC fabrics is that much of a problem, for reasons:

PVC is produced by experts that have taken all the necessary precautions for all possible reductions of safety risks it may cause in the lab or in mass scale production.
The process of synthesizing PVC is not a secret. If it was too harmful (rather than its profitability), then companies would have been banned from producing such a thing.


Phew, I thought there was something serious about PVC fabrics.

There is! The problem is not the process, but VCM and phthalates.
Issue 1: VCM
With a chemical formula of $\ce{C2H3Cl}$, a boiling point of $-13.9°C$ and an approximate molecular weight of $62.5 \frac{g}{mol}$, VCM is the raw material for PVC. According to here, the death of four workers had been approved due to VCM in 1974. (Though wikipedia says it was three workers dead) It's reported that in 1975, an annual 5-billion-pounds rate of production of VCM was confirmed.
The industry had the worst ways of producing VCM, and has suffered for decades until better ways of producing it have come around. According to here, a traditional way of producing VCM was the reaction of acetylene with Hydrochloric acid, as following: $$\ce{C2H2} + \ce{HCl} ~-&gt;~ \ce{C2H3Cl}$$
It was in the presence of Mercury(II) Chloride as a catalyst! Nothing has been done to reverse the harmful effects done to environment because of this very reaction.
In the modern process, &quot;polymerization&quot; is known to be the most dangerous stage and the peak of the overexposure.
VCM is believed to be carcinogen. Severe symptoms have been reported due to the overexposure of VCM; such as: Hepatotoxicity (liver damage and tumor growth caused by chemicals and more precisely, angiosarcoma).
Issue 2: phthalates
VCM is the fundamental raw material for the synthesis of all kinds of PVC; rigid or soft. But Plasticizers are being added to rigid PVC to &quot;soften it up&quot;; so it would be applicable for the future use as &quot;PVC fabrics&quot;. Phthalates are common plasticizers in the production of soft PVCs.

They are divided into two distinct groups, with very different applications, toxicological properties, and classification, based on the number of carbon atoms in their alcohol chain.

Phthalates aren't covalently bonded to the matrix of PVC. Therefore, the lighter ones can leach relatively very easy, usually due to heat or strong solvents.
The most common phthalate is diethylhexyl phthalate(DEHP). Studies show that Americans are exposed to DEHP. DEHP is believed to cause health complications in a variety of ages.
Oh, wait: Issue 3: PVC itself! But when it degrades
PVC is known for its strong linear polymer; but when it degrades (usually due to careless use or disposal) it degrades! Degradation is excessive reduction in a plastic's average molar weight. PVC will &quot;microcrack&quot; when it's degraded, into macroparticles that are a big threat to the environment. These particles &quot;soak up&quot; POPs and afterwards are usually ingested by living things, making it a big deal of our everyday plastic pollution exposure. (as wikipedia puts it)

What should I do now?! Panic?

Considering the advancement of technology and our anxiety to preserve our health we humans aren't sitting around to watch ourselves getting sick! I don't mean the hard-to-come-by sites that say overexposure to PVC isn't carcinogenic, but real efforts into solving the problem. News has been spread that REACH attempts to authorize DEHP and two other phthalates and ban their use in specific materials. DINP is another plasticizer, approved by the EU risk assesment, that will eventually replace the former plasticizers, hopefully.
Scientific researches for over ten years have proven that the amount of exposure to the chemicals mentioned is far from dangerous in current conditions and uses. So sit back relaxed; it's true that these dangers exist, but they're not serious threats to a healthy person, at least not yet.