There needs to be some commonly-accepted understanding of what constitutes legitimate grounds for offence. You appear (though I don't think this is what you really mean) to be saying that anything that is found offensive by someone capable of causing a distraction over the issue should be accepted as such and removed.
To be honest, 'bro' is not an important word to me. But I worry about what it means if we can't use even such a silly word, as a fairly cheesy pun, without it causing such controversy. It feels like rather than bringing people together and making them more tolerant, discussions like this are just dividing people, over what is really a pretty trivial thing. Are we all so desperate to tell each other how to think and act that we can't let a silly pun be just a silly pun? Do we have to accept that even perfectly reasonable people, capable of giving good reasons for their actions (such as your blog post title) ought to have to self-censor rather than ask others to take the thing in the spirit it was intended? A little charity on the part of the critics would be nice.