People who are involved in a zero waste lifestyle says they are doing this to save the planet. Is this a practical lifestyle, and are there likely other sources of pollution to which they are contributing?

One of the biggest problems that comes up in the course of answering this question is defining a "Zero Waste Lifestyle;" this isn't a prescribed set of criteria in the way something like the Atkins Diet or epilepsy are. The definition of waste itself is uncertain, and what one person considers to be "zero waste" is likely not to meet another's terms, in the same way that there isn't some sort of regulatory body overseeing veganism. More to the point, my own research suggests Wikipedia is the highest-authority source for information on the zero waste concept, and Wikipedia isn't the most reliable resource. I've linked the website of a zero-waste advocacy group as a source below, but keep their bias in mind. 
Zero waste, as a lifestyle, seems to be a fairly straightfoward concept; the individual generates no trash, or, more specifically, nothing that is a part of their lifestyle ends up in a landfill or incinerator. This immediately calls into question whether many of our typical behaviors are compatible; for example, biodegradable or reusable packaging is still relatively rare, and so this would eliminate things like plastic milk cartons or frozen dinners from the things a zero-waster would be able to conscientiously purchase. In this sense, it seems likely that a zero-waster would be obliged to either grow their own food, including animals, or would have to adopt a vegan or near-vegan lifestyle in order to avoid all packaged products, including packaging for meat.
Practically speaking, this would also strongly influence almost any other choice the zero-waster is able to purchase as well, since nearly everything has some kind of non-biodegradable packaging. In terms of a modern lifestyle, this would include things like mobile phones, computers, printer cartridges and cars (the maintenance, for example, would require oil, which comes in plastic containers). A significant degree of the modern lifestyle would be unavailable to the zero-waster unless they were willing to compromise their terms, such as by taking their car to an auto mechanic so that the "waste" was not "theirs," but the mechanic's. This would also call into question how any zero-waster is able to communicate on the internet without violating their principles by owning and accessing a device made with fossil fuels, powered by electricity produced by fossil fuels. Perhaps in these cases the zero-wasters considers it to be a "once, then never again" exception whose value outweighs the moral contradiction.
Furthermore, if the zero-waster lives in a developed country and makes use of its advantages, such as public transport, electricity, medical care, and public education, they should be considered to be de facto participants in any and all waste generation that society engages in. This doesn't diminish the value of any zero-waste choices over which they have direct authority, but they cannot claim moral superiority or exemption from participation in polluting activities.
In terms of this being a "practical" lifestyle, I think it would depend entirely upon what you're willing to give up in exchange for it. Considering that there is no immediate reward, it seems much more likely that the average person would consider it inconvenient at best, or impossible at worst. Its feasibility would depend strongly upon the availability and affordability of fresh, unpackaged food, a consideration that is likely to play out very differently for single educated people compared to families or those who live far from a grocery store.
https://www.theguardian.com/environment/2016/apr/22/zero-waste-millennial-bloggers-trash-greenhouse-gas-emissions