'Offensive' is a weird word. Many people find many different things offensive. Some pride themselves on being offensive. For some, taking offence is almost a sport, and for others, being cynical and remaining unoffended is a source of smug self-satisfaction. It is also an annoying container term that I wish could be ditched.
The reason why I want to distance myself from "being offended", is precisely because anyone can claim it, and often does so for the wrong reasons. It also implies that the "offender" should change something, apologise, recant, regardless of whether the offended party was right to be offended.
Now, this is a sensitive (!) subject, because we live in a world where advocates of inclusion, whether their focus is on social matters, gender or culture, get constantly told not to be offended, that "they didn't mean it that way", or have to deal with lame fauxpologies.
Context is everything, but let's take a hypothetical example. I believe that there is no God. Some theists will find this offensive, and a vocal minority will be outraged at someone openly stating their atheism in their presence. However, my not believing in God has no bearing on how they live their life. They can still go to church, rest comfortably in the fact that most people around them share their beliefs, and I don't tell these people they cannot believe whatever it is that they believe.
A different example is that when a woman causes a traffic accidents, some people will be at hand to - all in good jest, surely - blame the accident on the fact that she is a woman. That is really offensive, because it adds some more spice to the steaming dish of sexism and misogyny that our societies constantly have at the ready, effectively barring women from a not so insignificant number of domains, equal rights be damned.
There's another nuance that needs to be made. If someone was to say to me: "I hate straight, white people and I wish they would be executed" that is of course hate speech, but unless that person is directly threatening me or is in a social position to hurt me, it's nothing more than an empty - stupid as it may be - gesture. I would be right to take offence at the statement, but the outrage would be comparatively shallow.
Threat and power
Maybe it's more productive, then, to speak about threat and power factors in statements? An analysis of those will always be subjective, and possibly open to abuse from people who thrive on paranoia, but it at least forces participants in a discussion to look at a number of underlying facts instead of yelling "I'm offended!" and/or "don't be so easily offended!".
Another reason for writing this is because language that is fundamental to the cause of progress or the advancement of minorities is continually being re-appropriated by groups in power to portray themselves as the oppressed. This is clear from my example of the atheist statement - and I'll get back to things like this more coherently later when discussing rhetorics. Many American Christians do, in fact, falsely believe they are being oppressed.
What we should be asking
If someone says "I take offence at X", it's always a good idea never to summarily dismiss it, but I do believe it should be dismissed if it rests on nothing but false claims. Is there a question list we can tick off? Never completely, because each case is different, but a few questions might help:
1. What is the specific context?
2. Is there an implied threat?
3. Is there a significant power differential?
4. Is someone's freedom being restricted?
5. Does the statement inflict actual harm?
Come back later for more on rhetorics of progress!