First I'd like to say that I am a straight white male, but I don't think that disqualifies me from being able to answer. If it helps, I have two older sisters among many other female friends, my eldest brother is homosexual, my nephew has autism, and I have numerous friends of different ethnic backgrounds, all of which I love dearly. (stated to hopefully convey that I don't believe I am sexist, homophobic, racist, etc...).
The first point that I think would help your case is to not refer to other majority groups as "privileged." This has always irritated me when I hear someone refer to all whites or all males or any other majority group as privileged. There are many straight white males who certainly do not consider themselves privileged. Whether it be because they live in poverty or because of some unfortunate circumstances in their lives. I feel privileged to have a loving family but have never (and likely will never) feel privileged just because I am a straight white male. I've had my share of hardship in my life and someone telling me that I'm privileged won't ever do anything except irritate me.
As an example, saying:
You are privileged to be {some majority group}, because you don't have to face {some problem faced by a minority group}.
This makes me irritated that someone would say I am privileged simply because the problems that I have faced are different from the problems that they have faced.
EDIT(insert):
Most people the term [privileged] is directed to assume it means they were given something (e.g. a loving family), and that's not what it means in this context. - Beofett
@Sudsy1002 You and I are both white, and (I assume) both in the U.S. If either of us calls the police, it is likely we will be listened to and not suspected of being burglars in our own homes and not at risk of immediate violence, whereas African Americans face a different calculus when calling the police. This is what a lot of "privilege" is. When people hear examples like that, they say, "That's not a privilege, that should be the common decency every person gets!" That's the realization that (I believe) the term is meant to encourage, but your post makes it clear how the term can fail. – cactus_pardner
The kind of "privilege" described by cactus_pardner is much more agreeable to me. The issue is trying to differentiate between the definition that I would normally associate the word with and the example given above. The above example is a good illustration of what is trying to be conveyed while I think it is much more likely for the majority group to perceive the use of "privilege" to be the same as I did (meaning, to be given something). The point here is that the word "privilege" should be avoided while still trying to conveying what cactus_pardner has in his comment.
The 2nd point is about directly calling out racist, homophobic, sexist, or otherwise demeaning remarks. To be honest, I don't see these as being any different from calling out someone's actions for just being rude or offensive, regardless of what the topic is. Like the examples above, the first step is to not label the offender. If the offender feels attacked, then they will likely be defensive and/or attack back. A great way to avoid this is with the following statement:
When you do X, I feel Y.
or the reciprocal:
I feel Y when you do X.
The important thing is to be specific with what X is.
If someone says
All blacks are inferior to whites.
You will likely have the impulse to call them a racist (I myself would be outraged). That would be the wrong approach though. Remember, we need to avoid labels. Instead, follow the phrasing above.
When you say "All blacks are inferior to whites", it makes me feel like I am being discriminated against because of the color of my skin.
You can also add on at the end of that:
Is that your intent?
That should be a rhetorical question, but even if the person says "yes", then they have admitted that their behavior was directly intended to be harmful. You likely won't be able to fix people who are actively trying to harm others but you can make their actions visible to others who can see their actions for what they are. Hopefully they will answer "no" to the question above and be a bit more compassionate though. Note that the phrasing above does not say
When you are being racist, it makes me feel like I am being discriminated against because of the color of my skin.
The difference between the first example and this example is that you are explicitly stating what the other person/party said/did to make you feel bad without any kind of labeling or judgement in the first example. This is important, because you are not countering their hurtful remarks with remarks of your own, you are just stating how you feel and directing the comment towards their actions rather than them as a person.
You may feel inclined to be more direct about accusing someone of being a racist, homophobic, sexist, etc.. but those words are not just descriptors, they are also insults to many who would take offense to being labeled as such. Instead of labeling the other party, it is much better to call out their actions (again, using the phrasing of "when you do X, I feel Y").
The XY phrasing is not only essential to making the other party not feel attacked by what you are saying, but it also gives you a very specific problem to focus on. For instance, in the above example again:
When you say "All blacks are inferior to whites", it makes me feel like I am being discriminated against because of the color of my skin.
It is a lot easier to argue your point. The other party cannot simply say "you don't really feel that way" or "that is not what I'm saying/doing". Since you are pointing out explicitly what the other party is saying/doing, there is no room for argument, nor can anyone tell you how you feel, it is your feelings. This is different from the other example:
When you are being racist, it makes me feel like I am being discriminated against because of the color of my skin.
In this example, instead of explicitly stating what is being done, we are calling the other person a racist. This leaves them room to argue the point or simply so "no I'm not."
By doing these two things (1. avoiding telling others they are privileged and 2. using the XY phrasing), it will be much easier to have a conversation with someone about their behavior. It is a lot easier for a person to hear that their actions hurt you as opposed to them as a person being labeled as a racist, sexist, etc..
If someone is being hurtful without the intent of doing so, they will be much more willing to listen to how you feel rather than what kind of person you think they are. If they do have the intent to hurt you, I'm afraid there is little you can say to change them. Others will see the effort you put forth and will see the actions of those you interact with though, let them see that you were nothing but compassionate while the other party was nothing but hurtful.
This answer was in direct response to
When someone from a minority group says "that's racist/sexist/homophobic/etc" and the retort from someone from a majority group is, more or less, "no it isn't"
and the use of "pop-terms."
Those terms/labels can be insulting to many so it is best to avoid those terms/labels and focus specifically and explicitly on the actions that you found hurtful.