You should always care about how your posts might affect others
That is part of being part of a community. Words and actions have effects on people, and if we want to work together we should be trying to minimise the negative effects we have on others. That is part of being Nice:
Whether you've come to ask questions, or to generously share what you know, remember that we’re all here to learn, together. Be welcoming and patient, especially with those who may not know everything you do.
That isn't to say that it is always inappropriate to say something that offends someone, because that is largely unavoidable. But when people speak up and make their concerns heard you are expected to listen and learn and try to fix the issue if you can.
This isn't only to benefit potential people that might be hurt, it benefits you as well. Presumably you are writing something to say something, to communicate to other people. If you truly want to communicate with people effectively, considering how they might react to what you have to say is a very good step to take. And acting on those thoughts will help improve your communication with those people.
Of course this sets up a balance between what we want to say (and how we want to say it) and other people's feelings. And there is always a balance between the two. There's no clear point at which one overrides the other so we each have to constantly assess how best to handle the balance for ourselves and for our communities. But a necessary starting point is that we listen to each other when someone speaks up.
About the poem
This specific example you used a poem that unintentionally, to a good number of people (including myself), compared SE to Nazis and Monica to a holocaust victim. We don't allow people to compare people to Nazis for the exact reason that it never does anything good for a conversation. Additionally, this seemed like a poor comparison when talking about what ended up being a small online community and one prominent volunteer being arguably hurt. The hurt is real, but the comparison to the holocaust puts it over into inappropriate for me. And using such a loaded poem is unlikely to lead to any kind of productive discussion.
I'm not sure where you get the impression that everyone who disagreed with your posting this was part of one religion. You have no idea what religion, if any, I ascribe to. And it would be impossible for you to know that since I have never told you. (Hint: I don't fit into the box you painted everyone into). Assuming this is at the very least likely to lead you to the wrong conclusions about people's actions.
The better option is to actually listen to what people are saying. People opened up in the comments and let you know why they thought it was inappropriate, listen to them. Learn from them. Find a way to adapt your message such that it is not offensive to a significant portion of people on the site. You can easily convey the message of the poem without the controversy in any number of ways.
It's also worth noting that your answer had an issue at one point in where you were actively seeming to be aggressive towards people expressing disagreement for your use of the poem, and it remained up for a good amount of time which may have contributed to some people's view of the answer being rude. You did, however remove that line after it was pointed out, which was an excellent thing to do (and who among us hasn't written something out of frustration that we later regret?).
In the future, instead of pressing for deletion I'd rather someone was given (and took) the opportunity to rephrase and change their answer in response to feedback and thus improve it and their message. We should encourage people to do this when we think it might be productive or when something might be salvaged.