I'm amazed at how sensitive people are. Dirk had a cold. He's an all time great, and deserves plenty of accolades for overcoming that obstacle in an intense finals series. Dirk is also spot on that it was childish for them to make fun of it, but he quickly moved on, saying it wasn't motivation. He said, "It's the finals, who needs any more motivation than that?"
At worst, LeBron and Wade did something childish and random, and people react to it with statements like, as OP says, "this is exactly why so many people resented the Heat at the time."
What? First of all, put that statement into context. What else did the Heat do during the season that you sincerely believe made them earn that resentment? The Mavs legitimately had a guy on the team who got a championship trophy tattooed on his body before he even won one. The Mavs had guys on that team who were guilty of domestic abuse and DUI. No one cares about all that, yet Wade still has a reputation for being "dirty and douchey" as someone else in this thread wrote. The Mavs had their share of dirty and douchey players. It just wasn't part of the anti-Heat narrative of that chapter in NBA history.
Think about that for a second. "Some guy on the Mavs hurt his wife? Whatever, did you hear some guys on the Heat made fun of Dirk for having a cold?" Again, none of these things are good. But is the latter example that bad, in the scheme of things? It was about a diagnosed cold that by all objective indications was temporary and not the worst thing to happen in the world. Even Dirk essentially brushed it aside. On the scale of awful things to say about another player for an ailment, does it really rank so high? When Kenyon Martin made fun of Alonzo Mourning's incurable kidney disease, that was definitely not cool. Making fun of what was pretty clearly a 48-hour cold? Maybe not as bad.
On the other hand, I really don't think Dirk was the ultimate target of LeBron and Wade's childish act. It was more about the over-hyped narrative in the media of Dirk's cold. Every NBA player...from the stars like Dirk, Wade and LeBron...to Duncan and Kobe...to lesser known bench guys...have overcome immense adversity in big games. Much of the time, it either doesn't get covered, or it doesn't get discovered in the first place.
Heck, the Heat's Udonis Haslem was out all season with blood clots, and came back just in time to play 30 minutes a night in those very same Finals. The media didn't report it (or discover it) until 2015.
When Wade and LeBron were making fun of the cold, who they are truly peeved at isn't Dirk. It was the media. They aren't so much saying "Dirk's ailment isn't legitimate." It was, and I think they'd easily admit that. Instead, they are moreso thinking, "A bunch of us have ailments and adversity, Dirk included. Some the media is reporting. Some the media is not. Some the media doesn't even know about. It's a big deal for all of us."
If you cut through all of the over-sensitivity of the media and the fans, you're still left with Dirk winning a title, despite having a cold for a game or two, which is very noteworthy and respectable. I just don't think you need to over-exaggerate this one-off incident by LeBron and Wade as playing a major part.