The Aerosmith song "Dude looks like a lady" is not about trans people at all. It's about the singer Steven Tyler thinking a man was a woman from behind because of the long hair and tight clothes. It was inspired by Motley Crue because they wore lipstick, etc. So the song is not offensive to trans people. You simply misunderstood the meaning of the lyrics. I myself am trans FTM.

Several very important factors:

First, your excuse is inaccurate. Aerosmith themselves claim that Motley Crue’s contribution was how often they’d exclaim “dude!” while hanging out, and that the song was inspired by a trip the transgender bar in NYC.

Secondly, even if the song were inspired by Motley Crue wearing makeup, the lyrics say literally nothing about this being a case of mistaken identity. It goes into detail about Steven Tyler getting busy with a girl, and then she reveals a penis and tries to “blow him away,” which the context leaves unpleasantly undefined.“Never judge a book by its cover,” “body of a Venus,” and “her love in disguise” all directly imply someone presenting as a female, not a feminine-looking man. If the song were meant to allude to a feminine man, then their choice of words should have said something about that.

Third, even if the were inspired by Motley Crue and the lyrics were actually referring to an effeminate man, the song still leans on transphobic tropes and pushes the “trap” mentality that at any moment a hot woman could spring a penis on an unsuspecting male and that Tyler is the victim in all this. And in the 25+ years since its release the song has been used to insult and victimize women regardless of its intention

Fourth, I don’t care if you’re FtM. This is an issue of transmisogyny, directly targeting and insulting trans women, and as a man you have almost as little authority to tell me what is and isn’t offensive to trans woman than a cis man.