Having covered both character loss and (supposedly) irreversible characters before, there’s only one obvious issue less to cover about these kinds of characters. And that is the effect such losses have on systematic relationships, or perhaps rather, how people can perceive them. It may seem intuitively obvious to readers here (because most of them here clearly know their biology) but just because whales do not have fur does not make them not mammals and just because penguins can’t fly does not make them not birds. However, if you are not aware of how such relationships are assessed or what these characters mean and how evolution works.
The most obvious point is that at least some of these characters are not really used by biologists. ‘Flight’ is not really something you can use in itself since it’s as huge combination of anatomical and physiological characteristics so it’s a poor choice. Secondly, losing a couple of characters is normal over the course of an organisms’ evolutionary history – snakes have lost their legs, tyrannosaurs lost a few fingers, kiwis got rid of their arms and so on. This doesn’t change the rest of them, and it’s really very common.
Finally, as an extension of the second point, single characters don’t really count for much when it comes to assessing relationships. As I have stressed before (and indeed as others have before me) details matter and you have to take into account all of the available evidence. Whales are still mammals because despite the loss of the hindlimbs and hair, they still have mammary glands, a mammalian inner ear and various other characters. Penguins can’t fly, but they do have air sacs, beaks, feathers and more. To get fixated on a single character is to assume that the others are either not important or less important and to ignore the other evidence.
Things change over time and some animals have become modified to quite a profound degree from the ancestral condition, but this is ultimately what is important. Ancestrally mammals had hair and this remains a useful character to define the clade even if some don’t have it anymore. Snakes, though they may not look it, are still tetrapods.