or function doesn't seem to be working as expected

I would strongly suggest steering clear of using dot notation when you want to get information from somewhere. My general rule of thumb is:

• If getting information use index() or property()
• If saving information use dot notation or square brackets and quoted fields (Don't know what to call this but it would be something like ["createdDate"])

Dot notation doesn't have inbuilt handling of when the field doesn't exist. When you use the function rule!UW_GetRequirementActivityByType(fv!item, or("WITHDRAWN", "ACCEPTED")).createdDate, you are saying "give me the createdDate field please" and dot notation can't handle if the field doesn't exist.

Using the index() or poperty() functions on the other hand, such as property(rule!UW_GetRequirementActivityByType(fv!item, or("WITHDRAWN", "ACCEPTED")), "createdDate", null) says "give the createdDate field please, and if it doesn't exist give me null".

So I suspect it has nothing much to do with your or() (although it could, I'll be honest, I didn't go through your code!).

If this doesn't solve your issue I'll take a deeper look.

EDIT: I have some further feedback

1. I definitely didn't answer your question. And or() outputs a boolean and must have a true or false argument inside it. What you're saying is you want the input to be either "WITHDRAWN" or "ACCEPTED" but you've made no comparison and even if you had either "TRUE" or "FALSE" would be passed. I've left everything else I've said though as it is relevant and see code below for how I would fix it. I'm going to assume that "inputTwo" in the UW_GetRequirementActivityByType rule can accept arrays.
2. If you find yourself repeating something over and over again there is likely a better way of doing it. You use the UW_GetRequirementActivityByType function over an over again with either similar or the same inputs. If this is a database call, WebAPI call or really anything you're getting the same info over and over again and as a principle this isn't so great. I'd suggest refactoring to the code below. There may even be more efficient ways depending on exactly what you're doing and what's being called but this is at least a step in the right direction. I've also swapped your dot notations to index() or poperty(). Be especially careful calling something within a a!forEach() loop! Things can quickly get out of hand and performance suffers. Essentially if you're calling the same information more than once there is a better more performant way to do it. Some situations matter more than others but if you don't practice the principles on the basic things you aren't likely to get them right when it does matter.
3. ALWAYS use key value pairs. Your rules will have rule inputs, use these when calling the rule. I can't fix this as I don't know what your input names are but as a demonstration I've named them "inputOne", "inputTwo" etc.

a!localVariables(
  local!requirementsResponse: rule!UW_GetRequirementsByCase_RDS(
    inputOne: "SomeKey"
  ),
  local!requirements: {
    a!forEach(
      items: local!requirementsResponse,
      expression: a!localVariables(
        local!receivedRequirementActivity: rule!UW_GetRequirementActivityByType(
          inputOne: fv!item,
          inputTwo: "RECEIVED"
        ),
        local!withdrawnOrAcceptedRequirementActivity: rule!UW_GetRequirementActivityByType(
          inputOne: fv!item,
          inputTwo: {
            "WITHDRAWN",
            "ACCEPTED"
          }
        ),
        a!map(
          type: property(
            fv!item,
            "name",
            {}
          ),
          status: property(
            fv!item,
            "status",
            {}
          ),
          orderDate: property(
            fv!item,
            "createdTimestamp",
            {}
          ),
          orderRep: property(
            fv!item,
            "requestedBy",
            {}
          ),
          receiveDate: property(
            local!receivedRequirementActivity,
            "createdDate",
            {}
          ),
          receiveRep: property(
            local!receivedRequirementActivity,
            "creatorFullName",
            {}
          ),
          resolveDate: property(
            local!withdrawnOrAcceptedRequirementActivity,
            "createdDate",
            {}
          ),
          resolveRep: property(
            local!withdrawnOrAcceptedRequirementActivity,
            "creatorFullName",
            {}
          ),
          resolutionStatus: property(
            local!withdrawnOrAcceptedRequirementActivity,
            "type",
            {}
          ),
          resolutionNotes: property(
            local!withdrawnOrAcceptedRequirementActivity,
            "commentText",
            {}
          )
        )
      )
    )
  },