Given the historic (and current) imbalances of power that often exist, on a societal level, between men and women, there's a difference and while it's easy to make the comparison as has been done, it's not particularly accurate nor equal.
I don't mean to be rude but you're basically attempting to justify a double standard, and double standards are always bullshit.
There might be at least one or two flabby, pasty old white dudes who are insecure enough to be turned off by the Dad Bod can. You might also think their feelings are ridiculous, but that's no different than Blasphomet thinking that the people offended by the NN/Immodest cans are being ridiculous.
Real, actual feminism requires equal treatment for both sexes. Otherwise you're just tilting the scales (which were previously unfairly tilted toward the male side for literally all of human history) towards the female side. If the NN can is offensive enough to be changed, then I don't see why the Dad Bod one isn't. Disclosure: I don't actually care either way, I just feel that what's good for the goose is good for the gander.