Should I continue to hand feed?

If you weren't feeding him, would he be able to able to prepare dysphagia compliant foods himself?  

One of the benefits of your availability while he's eating is to monitor the existence and level of choking, noting when certain foods may become too challenging to swallow, depending on the dysphagia stage.

Since he apparently has a dysphagia diagnosis, I'm assuming you have the dietary charts identifying the different levels and foods which can be used?   If not the speech therapist or whoever performed the swallow study and diagnosis D/X could arrange for you to get these.  They're invaluable in managing dysphagia.

Yes, it is a problem to hand feed in that it enables a person to give up on activities of daily living. A person should be encouraged to feed him/herself when at all able. That said, if a person is not going to eat, and if your feeding does result in a better intake, then there is no harm in helping with meals if you are able to.
I would caution not to feed when a person is tired, very weak, or unwilling. If you do so the difficulty with swallowing can worsen, resulting in swallowing food into the lungs and aspiration pneumonia.
Your father is 90. I would encourage you to allow him to eat or not to eat as much as he wishes/does not wish to eat. I hope he will continue to improve. Goodness knows he is getting dedicated and loving care. Your Sister and you are providing this, so don't allow yourselves to be divided with any silly bicker like this one. You are BOTH RIGHT!

First I must ask, with your fathers dysphagia are his foods being pureed and his liquids thickened? If not that could cause a real problem and aspiration pneumonia, which more times than not leads to death. So make sure that is being done.
I know all about that as my husband almost died after having aspiration pneumonia, and came home completely bedridden after that, and I had to puree all his foods and thicken his drinks with the product Thick-It.
I think at your fathers age, if you feel better feeding him to make sure that he's not choking on anything, that is perfectly fine. It's not like he's 50 years old, he's 90 for crying out loud. And at least then you know exactly what he is eating and that he is in fact eating at all.
So ignore your sister and keep helping your father any way you see fit to. I'm sure he appreciates all you are doing for him.

Is your sister right, can he really feed himself? I had to feed my mother for several years before she died, although she could handle finger foods she couldn't manage cutlery and never would have been able to take in enough calories without help, insisting that she feed herself would have been neglect.