would, is the friendly manner, how you would talk to just about everyone on the planet can, is a bit confusing as it can mean the technical (are you able to) but some people confuse it with a request must, is an very firm statement and can be seen as an instruction (in fact legally it is) in this case "that must be my pleasure" is just wrong but seems to suggest that doing so is the individual's only pleasure from the task rather than say being with Allen so it rude. If the term passive-aggressive means anything to you this is straying into that.

It is depends on the situation but it is "That would be my pleasure" . One doesn't have to or must do anything in this case it sounds like. Example: In school I must do my homework. Would you like to go with me? I must go with you as my mom isn't here to get me from school.

"That would be my pleasure" is a fairly normal expression of politeness, subjunctive mood, I suppose. I cannot recall hearing anyone say "that must be my pleasure". Any introduction of uncertainty or possibility in a situation increases the level of politeness, like asking "could you open the window?" rather than "can you open the window?"