It's not like Alice or Bob actually believe in an epistemic sense that some line of the other's argument is wrong. Rather, the other's argument makes them feel uncomfortable, because it is in some way related to something personal.

I think that in many situations which pattern match to these, this is Bob's view of the situation but not Alice's, which contributes to the situation. Bob thinks that Alice only disagrees because she is upset, and so doesn't actually consider her point of view seriously. Alice then finds the discussion difficult not only because the topic is upsetting, but also because she is very clearly not actually being listened to. Given how much more difficult Alice finds the discussion than Bob, she will likely not express the points she's trying to make as fluently or eloquently as Bob argues his side, adding to her frustration and strengthening Bob's view that he's right and she's just too emotional to see it.

You switched Bob and Alice between examples but I think the point is clear. As one concrete example, Example 4's Bob may not be a consequentialist, or he may feel that under moral uncertainty it's worth taking rights-based arguments extremely seriously even if otherwise acting as a utilitarian most of the time.

Thanks for writing about this, I sometimes find myself in similar situations to your examples and feel unsure how to deal with it best.

I just read Cullen‘s post about psychological harm and thought I‘d mention it here because I think it explains part of why I sometimes experience less patience than usual when it comes to psychological harm that seems partially induced by ideological origins. https://forum.effectivealtruism.org/posts/FpMjQWaNvcPKPuhXQ/blameworthiness-for-avoidable-psychological-harms

So I wrote some practical advice below. 

I think the author of the post seems pretty thoughtful and sophisticated, so maybe this is too basic or not what they want. 

But it is hard to be informative as there is a lot going on in possible answer:

• Are Bob and Alice friends or just acquaintances?
• Are they discussing views, or are they working on a project together?
• What are the power dynamics between the two?
• Are they communicating 1on1, or is there a performative aspect, e.g. Alice or Bob's opinion is dominating a group discussion?

I think Example 4 seems tough, and I'll give one way I would approach this. 

Example 4 - Caring about Animals:

Bob loves animals and has been vegan for many years. He notices that he gets angry that Alice argues that way, even if he can't pinpoint, why he thinks she is wrong. He wishes that Alice would just go with "These were animals once. With experiences. So eating meat is obviously wrong".

I think it is important to avoid conflicts, confrontation or enforcing views about improving animal welfare with people in animal welfare.

There is a long history of conflict between approaches or viewpoints in animal welfare movements, which is wasteful. 

I think animal suffering is so abhorrent that it makes many points of view reasonable. Alice's "rationality" viewpoint can effect change, and Bob's "emotional" viewpoint is understandable if you take animal sentience seriously.

Maybe use a preamble? 

I think one way to begin any emotionally difficult presentation of a strong view is to use a preamble that genuinely accepts the opposing viewpoint before making your own point. 

For Alice, she could say:

"I think that animals are sentient. They have souls. I know Bob knows this.

"I want to talk about [ content such as impact] because I think it can make a bigger impact for these animals, this is...[ begin content ]"

Some comments: 

• I don't think the example here is perfect. But even this simple preamble as long as it's genuine, seems to help a lot in difficult conversations. Saying something like this is easy once you practice it a few times. Because it's easy to say you can do it under emotional strain.
• When things are really emotional, using informal language, and directly addressing the person are good strategies if it can be done naturally and genuinely. In the example, it tries to finds common ground (helping animals) and specifically acknowledges what Bob wants or feels.
• When things are difficult, saying that you are upset explicitly due to the immediate circumstance often works well, and senior and powerful people do this.  You can say, "Look, this is an emotional subject for me and I'm upset about it. Now...[begin preamble]". It's still important to preserve gravitas and decorum, so be brief and state this unemotionally.  It's sometimes OK to be more defensive, and weaken the emotional aspects and use formal words you wouldn't normally say: "I find this untoward and problematic...".

It's possible that giving a preamble or communicating is not practical. For example, you may not even get a chance to make a long comment. 

If this is the case, or if both Alice and Bob are highly emotional, the conversation probably is not going to work and it's better not to do this. 

If there's resentment from past actions or a sense of underhandedness by either party, this makes a preamble or any communication difficult. In these cases I find resolving the issues as a whole impractical, and it's not going to work.

Not everything works, it's OK. You can walk away, or there's other approaches you can take.

I think modesty goes a long way here. This is both in not enforcing your views onto others unless necessary, and also accepting views. 

There's a lot of emotional labor and empathy involved. Your energy is a limited resource. You don't have to do this or other efforts if the other person isn't listening or simply doesn't get it.