Just chiming in as I believe I may have had a notable roll in convincing people that Dawn (and similar) are not the magic stripping solutions that they were once touted as.
First off, you could call it a degreaser. Of course the same arguments can be applied to most car wash products, glass cleaners and such. In the case of Dawn, it is a mostly neutral blend of surfactants. The surfactants are specifically intended to act upon oil soils and thus can be considered degreasers (if you wish to take it to that extent). It follows that almost anything that contains surfactants could thus be described as a 'degreaser'. So I think one needs to take care here. Dawn and similar will intentionally be mild because they need to be safe for repeated and prolonged skin contact. Let me guarantee you Dawn has been much much more thoroughly tested, in this regard, than any 'car shampoo' product on the market. I might hazard that Dawn has been more thoroughly tested than almost every car shampoo when added together! This skin contact thing is important because you cannot have excessive degreasing character - it would result in oils being removed from user's skin which would lead to all manner of skin conditions and irritation. Trust me, this does not happen with Dawn. Car shampoo, well there is another matter altogether. As above, there won't be a single one on the market which has done testing, on the level of Dawn, to demonstrate the mildness. I am not saying that they are needlessly aggressive, but it is simply wrong to suggest that Dawn is a notably more potent degreaser than your average car shampoo.
Moving on, in the same vein, the colloquially termed 'car soaps' are often much more potent degreasers than a Dawn type product. Often this term can be used to describe notably alkaline and solvent containing products and it should not take a rocket scientist to appreciate that there is a good degreasing capacity there. Overall, I would just like to encourage that we stop trying to vilify Dawn because "it's a degreaser and my car soap is not" - in the vast majority of cases, this simply is incorrect.
As for how Dawn does actually behave - other have already linked to threads where I have made big contributions on the subject. Briefly, Dawn (and other good washing up products) will have a characteristic which is mostly ignored - they will inhibit water spotting. This is essential in the primary application because water spotting makes dishes look dull and not properly cleaned. The way that this is achieved is by the use (mainly) of surfactants which will basically stick to surfaces. They (temporarily) adhere and they ensure that water on the surface forms a sheet (this is a hydrophillic surface where water 'sticks' - not the commonly discussed 'detailer' sheeting where you have a moderately hydrophobic surface where the water runs off as a sheet, as opposed to breaking into beads as would be seen on a more hydrophobic surface). In so doing, the water evaporates away evenly and you don't get spotting. This is the reason why you don't get dishwash products which make the water bead, it is just a bad idea. Anyhow, this then transfers to your automotive use. The same thing applies, these surfactants will adhere to your paint and will tend to make it look like the surface is no longer water repellent. In fact the reality is that your LSP is almost certainly still quite content, hidden under a temporary layer of surfactant. I have repeatedly confirmed this with so called 'stripping solutions' where I have been able to show a big degradation in the beading which can subsequently be recovered with a quick IPA wipe or a very thorough rinse. Others can attest to the same results (which is probably why we got traction with the concept!).
For my part, this sort of behaviour should actually be desired for a detailer. Like with a dish washer, it will decrease the tendency towards water spotting (and we all know that water spotting is bad). Unfortunately, I know of nobody who actively pursues this for a general purpose car shampoo because many users will (wrong) perceive that their LSP has been harmed. In fact, I am fairly confident that the few products out there which do behave in this way are, either knowingly or otherwise, sold as strippers (and I have yet to find one which genuinely is).
So you should not fear Dawn or similar products. The majority of the cleaning capacity will be provided by chemicals which are the same or comparable to those in your auto specific products. The apparent diminishing of water repellency is very likely going to be a misunderstanding, thanks to Dawn being specifically designed to inhibit water spotting.
That is my take on it, your mileage may vary, of course! For anyone reading and thinking you might like input on any similar topics, fire me a PM if something comes up. Life is somewhat busy these days so I don't get as much forum time as I might like!