If not, why would he apologize?

Yeah, is your DH nasty to you? If not, and it was just a typical marital squabble, then he shouldn't apologize. In fact, you should ask your son to apologize if appropriate. 

Perhaps your son's mental illness makes him misjudge people's behavior? 

"The next day we decide my husband should text him an apology of some sort. Just to cool things down. He texts a nice note and within a second is texted back F$&@ off!  I am appalled. "

OP explained that and sometimes you do apologize even if you have done nothing wrong, if someone is upset to smooth things over and move on.

OP I realize he is 26 but because of his autism and mental illness I think it is appropriate for you to try to intervene and get him some help. 

Maybe you could talk to his father not sure of your relationship with him but maybe see what he thinks since he lives with him all the time.  But either way talk to your son about talking with a counselor or a doctor and see if there is something he could do to feel better.  Not because of the situation you described but because you explain his issues and that he is dark and depressed.  That is no way to live. good luck

I have anxiety and OCD quite badly, and I am a great believer in that mental illness does not give you carte blanche to act like a dick, neither does autism.   I think you should still send him a gift card.  However, I don't think you should ask him over when DH is not there, and any invitation for Xmas should have the proviso that he behaves in a civil manner to DH.  You and DH should present a united front.  

Appologies without infraction are bullshit. Don't play the bullshit games.

I agree with a couple of things already stated but will reiterate them with my own summary that it is all about communication.

1. I do think you should consider how you and your husband communicate, are you considerate of each other? Why do big meals make you two bicker/argue? Is the way that you express fustration between you healthy? Do you call each other names when you argue? Do you use bad language? Would you allow anyone else to talk to you that way? If you two could improve your communication styles so that you have a stronger realtionship would that be worth it? Even if it is just average marital stuff, why not try to improve things? I know I am not great in an argument sometimes.I have improved a bit over the years, but still get carried away when I am upset. If one of us says something particularly upsetting during an argument my husband and I will talk about it later and strive to be fairer to each other when we argue in the future. 

2. I think you should also improve how you communicate with your son. You had a problem with your son, but rather than address it with him directly you got your husband to apologize for something that you claim he should not have to apologize for. I am not sure what not sending your son a gift card for the holidays says to him? It is not a clear message and does not help in any way to move things forward in a positive manner. Have an adult conversation with him (understanding that he is now an adult and not the child he used to be). Tell him that you would like him to offer to help with cooking or chores when he visits,  and how you were suprised that your argument with your husband upset him so much and that you were disapointed in his response to the text he sent. Do not treat him like a child expecting him to either fall in line and apologise or to storm off. Really try to open up a little and try to uderstand each others point of view before making couterstatements. Life has changed a lot for you two over the years it seems and it feels from your post that you have drifted apart. Take some time to try to reconnect. I do not know that much about autism, but if these types of conversations would be difficult for him then consider having an e-mail exchange or uisng a therapist to help you two have a productive conversation. 

Trying to re-build a connection and establish better communication will help a lot more with your son and your husband than thinking that depriving a 26 year old man of a gift card will teach him a lesson or improve your relationship. All it will do is save you a few $$ and might make you fell a bit better for a short time. If you actually talk about the issues with your son and still decide that you do not want to give him the gift card, you can tell him why so that he understands the significance for you. 

DH and I bicker at the holidays due to stress and differing opinions on how things should be done. It happens. Unless your DH was cussing you out and calling you names, I'm not seeing the issue.

Personally, I'd have a chat with him and tell him he can either be family and act like it, or he can be alone. I had to have this conversation with my sister when she wasn't handling her mental health appropriately. I took her to Panera and had a very frank conversation with her about how she had to make a choice. She can either be angry about the past and cut everyone off OR she could recognize that it happened, set up appropriate boundaries, and not use the past as a weapon when she didn't get her way. I ended it by telling her I loved her, but if her plan was to be a little sh*t at Christmas that I didn't want her to come. I didn't care if she chose to cut us off or if she chose to move forward, but constantly punishing everyone because she hurt (and not letting ANYONE help her fix it) wasn't fair.

She decided to set new boundaries and behave. I love my sister and I'd give her a kidney, but the ups and downs were just too much. You should have a similar conversation with your son and be willing, for the protection of your DH and others, to disengage from him. That doesn't mean you stop loving him. It doesn't mean you don't help him if he is actually helps himself. It just means that you won't wrap yourself up in his drama and won't let him hurt others because he's mad.

Mental illness is not an excuse to be an arse. I have learned when my mom and sister are behaving a certain way because they can't help it (i.e. it's a symptom of their mental illness) and when they are just because they think they can get away with it. You likely know when your son is actually having problems and when he is just giving in and being an arse. Don't allow the latter to become acceptable just because he also suffers from the former.

The next day we decide my husband should text him an apology of some sort. 

Hubby should have never been in the position of appologizing to your kid, DH did nothing wrong.  It should have been you as the parent dealing with your own offspring.  I have two sons on the spectrum and work in the health field so understand behavioral outbursts quite well.  I don't think excluding or punishing anyone on the holidays is a good idea. It would be good to talk to your son, explain that you and DH squabble sometimes and it's normal for the two of you.  Good behavior needs to be reinforced, and it's your son who should be offering up an apology.  He may not have a warm fuzzy relationship with him but he does need to act like a grown man and be respectful.  

So I won't bore anyone with details, plenty of history in my blogs and posts.  Reading through, it sounds like you and DH may need a good counselor to work with you on communication techniques for ASD.  I spent 4 years in hell stewing and becoming negative and resentful.  Your DH could be in a similar place to me just before that spiral started. 

My SS is now 28 ... a few things are allowing me to overcome the negative period and the bad damage to my marriage. First is that I was 100% blaming my SS's behaviors.  In reality, it was 50% DW and I not setting boundaries and not discussing this all in depth, etc. as well as her very strong Concierge behavior.  The other item was in discussing some of the ongoing and annoying behaviors with a counselor, it seems SS28 is very likely in the ASD spectrum (previously Aspbergers) and studying the condition is helping.

Also, have zero doubt that a son with ASD no matter how caring and smart can and will resort to physical violence if triggered.  Yes, I got sucker punched by a 24 year old for telling him he should absolutely not be talking so mean to his mother at Christmas.  Fortunately, I did do MMA for a while and can take a hit and I did far worse than strike back but instead forgave and told him I loved him.  Yes, that was near the start of my 4 year emotional spiral but things are coming back.  No aggression since but I watch and can see how quickly he becomes angry at items outside his control. 

It is not easy working with a family member with ASD but working on common ground with DW, preventing and openly talking about Concierge behaviors and working to learn about ASD have really been a big asset to my life. I hope the same peace of mind for you and DH Without the spiral of negative years.