Outstanding objections appear to me to boil down to two points:
1) Some transactions cannot comply with this BIP because there are input and/or put index dependencies.
My response: No big deal, it's informational. They simply won't be compliant with the BIP, and that's fine with me.
2) If we set a standard now for transactions that is not apparently random ordering from the perspective of passive blockchain observers, transactions that can't comply with this BIP will stand out. Also, if we change our collective minds in the future about how ordering should be handled, those future transactions would stand out. Therefore, the "safe" course of action is to come up with another scheme that appears to be random ordering from the perspective of a passive blockchain observer.
My response: Apparently-random but owner-verifiable ordering is doable. Discussion of this has revolved around what I have called a "sorting key" -- sort lexicographically, and then reorder according to the bits in a sorting key that is impossible to predict by an attacker. This means passive observers cannot determine anything meaningful about the transaction (e.g. which output is change, information leaked based on utxo selection algorithm for inputs, etc.) but the owner of the funds and the sorting key can verify that his transaction matches the canonical specification. Ideally, I think the key should rotate for each transaction to avoid the possibility that a static key can link multiple transactions together. The key should be rotated in such a fashion that the next iteration is not predictable to anyone except the key holder (e.g. put the key through a secure pseudo-random function for each new iteration). This could be done by generating a few bytes of entropy upon wallet creation and keeping track of the current iteration of rotation. HD wallets could derive the initial state of the sorting key by deriving it from the HD seed. There are a variety of schemes that could work here.
My main objection to this family of approaches at present is complexity. I suspect that many wallet clients will not want to implement the BIP if they have to maintain a sorting key.