I think it's a little more delicate than some pensioners wanting to run their kettles back and forth.
I think most of the objections will be centred about forever cutting off one of the first passenger stations that started the mainline railways in Britain and that remains in nearly original condition and building over a bridge constructed by George Stephenson.
Edit: having read the proposal, they're not against the chord, just against the proposed ridiculous big arch design and subsequent dismantling of various grade 1 listed buildings. Can't imagine why, After all demolishing the Euston Arch brought nothing but benefit.
I dont think you can have read the proposal very carefully, as there is no plan to dismantle any grade I listed buildings. Only two structures in the vicinity are grade I, Stephensons bridge and the Liverpool Road station (with associated warehouse), and the Chord avoids both of these. The bridge will in fact be improved by its restoration to its original condition, with stone parapets on both sides.
As for the ridiculous big arch design, English Heritage actually said in one of their early consultation responses:
we can find no suggestion in the Scoping Report that any consideration is being given to creating landmark new bridge structures of exceptional design quality to carry the proposed new line over the River Irwell and the Inner Ring Road. This might, it could be argued, provide some mitigation for the significant harm which will be caused to historic assets and to their settings by the construction of the Ordsall Chord.
(Scoping Opinion: Proposed Northern Hub: Ordsall Chord, March 2012, p. 47).
After NR followed this advice and produced a landmark design, EHs position changed, but I think the original position was correct, and that the bold design is indeed a worthy addition to the collection of other bold railway structures in the area.
To my mind, while there certainly is a big impact from driving a two-track railway through a historic collection of structures, this has been very carefully assessed by the proposers, who point out (as kevconnor just did) that the builders of these structures did the same thing, radically altering their earlier interventions as well. Adding a metal extension to the Stephenson bridge, pretty much destroying the view of it from the north, would for instance no longer be countenanced but that is what happened in 1860, which NR now proposes to reverse. The whole area is a complex of layers of infrastructure, each of which has impacted significantly on the previous one, but the net effect (seen in the exciting views of bridges you get from the Castlefield basin, for example) is a set of structures whose real historic importance lies in their recurrent layering. The Chord, by adding to this, actually remains true to the historic pattern.
The impact on MOSI shouldnt be dismissed, but also shouldnt be exaggerated. The steam train ride is an additional attraction to the museum but its value needs to be balanced against the value of the Chord. Main line access, their other objection, is hardly ever used, and isnt preserved anyway by the alternative proposals.
Im generally supportive of heritage concerns, but here the narrowness of EHs remit stands out clearly in contrast to the broad scope of NRs preparatory work.