First of all, as a minor you can pretty much get a tattoo anywhere in the US as long as you have parental consent. So, legally, tattoos are not considered worse than "other things", no. The people up in arms over gender affirming care for youths should also threaten and harass tattoo parlors that allow this horrible, permanent body mutilation to happen to children. Laws should be passed around the country with as much vigor and urgency as with laws against trans people, but they're not. For some reason. I can't possibly imagine why.
If your argument is that it's hypocritical for a parent to refuse to let their child get a tattoo, but they're okay with them getting gender affirming care, then you've missed the mark on that one too. Unlike tattoos, that have no value beyond the aesthetic, gender affirming care actually improve the quality of life for the person, reducing depression and the risk of suicide. It's considered healthcare. That's the argument you need to be fighting, not these strawmen ones. But I guess that's not as easy. If tattoos were as important to a child's well-being as gender affirming care is, then this comic would be making a perfectly valid point, of course. Come back when that's the case.
I actually kind of agree with you when you say that young impressionable people should be protected from making life-altering decisions about their bodies in case they end up changing their minds. But the reality is that de-transition rates sits around 1%, and the most cited reasons for de-transitioning seems to be pressure from parents, harassment and discrimination. It seems like when it comes to identifying as trans, people actually seem to be pretty sure of themselves. If the de-transitioning rate all of sudden started SKYROCKETING then we should absolutely be re-thinking things. But as of now, that just isn't the case.
Edit: the de-transition rate is magnitudes lower than things like knee surgery and heart surgery. Surgeries people generally feel very positively about in terms of helping people. Why can a child get a heart surgery - something that isn't remotely controversial - to save their life, but not a child getting gender affirmative care to keep them suffering and from killing themselves?