Agreed, I have hit this when accidently making the wrong opponent move
Feature request - ignore moves if out of sync
I resigned two games for this. One time I misheard Rh3 for Re3 (please also check this question), one time I was just not careful replaying the correct move. A bit of a cold shower trying to find the best move and on the next move the opponent snaps a piece for position out of sync.

The game absolutely shouldn't accept a move if your board is not in sync, that seems a huge error. The fact that it is not accepting your move should also give you a clue you have made the wrong opponent reply.
Hopefully they will make a change. It might be worth making an official support ticket on thsi also
In my opinion, for this reason, the integration at the moment allows no competitive play. No advertisement, really, but the Acid Ape Chess App shows this is possible.
In the example, after replaying e5 incorrectly as d5 on the board, the app indicates this. It also ignores the subsequent move g3, as should be. One cannot continue without position correction. The above mishap is not possible.

As an aside I wish you could use AcidApe Chess to play here instead of jsut that other big chess site
The Acid Ape Chess is not free, and DGT board support costs additionally, unfortunately, right. But that is not my point. The Acid Ape Chess does not allow play on chess.com, so it does not provide an alternative solution to the problem, free or unfree.
My point is that Acid Ape Chess shows that the requested feature for playing online is possible.
So, such a feature seems to be possible on chess.com as well.

I contacted them asking if they were planning on adding support for chess.com. The short answer is no. They were a little rude about it also!

It's a shame as it's s an awesome app, it's great to be able to use the Dgt board by just connecting it to my phone rather than setting a laptop up.
Thanks for the information, good to know. There are a few responses on the review page of the google play store by the company. The responses there are partly also direct. Just search for "Acid Ape Studios" on the page. There is also an explanation regarding pricing of the app.
@BaronVonChickenpants On a basic technical level, I can add a few points here. The DGT LiveChess software is providing a connection through the board using the browser. That is why DGT LiveChess must be running while playing on chess.com. The Acid Ape Chess software is accessing the board directly over Bluetooth or USB, which is an entirely different way to speak with the board.
To implement support for chess.com for the Acid Ape Chess requires supporting a very different interface (the web interface), which is undoubtedly a lot of work. For this reason, I understand the app does not support playing on chess.com.

I understand that, but it seems to me ( as a layperson here) that the hard work of talking to the board has already been done, whjat remains is a method to transmit those moves onto the chess.com server, and to retrieve the moves played.
Regardless the AcidApe people seem very set on not doing this , and get quite angry when asked

I understand that the board just gives information on the board position, its up to the client to determine what 'move' was made. However, that is also already being done for them to be able to push the game moves to lichess. The client is already reading the board and determining what the actual move made was and then pushing it to a server. All that work deciding when a piece has been still long enough, and of the move is a valid move and all of that is already happening. None of that side of things would need to change in order to pass those moves to a different system
While I'm sure that pushing moves to and from a different system is no piece of cake the part communicating with the board to get the current position and interpreting that as a move to play is already working, and working well. It seems to be that what is needed is a way to emulate however the move currently gets from LiveChess into chess.com and back again.
Its a bit of a moot point though as my support responses from AcidApe make it abundantly clear they have zero interest in speaking with chess.com on how to integrate with the existing LiveChess system so I doubt it will ever happen.
@BaronVonChickenpants Sorry had a problem with my previous message (which you reply above), so reposting it below.
I understand that you need to make an assumption, but I can assure this assumption simplifies things too much.
The board cannot just spit out the moves made. I make a basic example, which does not cover the full situation, which I don't even know.
If you move the rook from a1 to a8, leave it there for 0.2 seconds, then move it to a7, leave it there for 1 second. Is the move now Ra1a8 or Ra1a7 or something else? Move determination is at the software level and, as such, not inside the board. However, the board can make some determination, which is not always applicable. The board, in principle, only gives the changing positions. Also, movement detection is different for OTB and playing online. When playing OTB, the one move must only be finalized when the opponent moves. So one can move the rook up and down forever and assess the move only when the opponent moves. For online play, one needs to deliver a move to the server in time. One must determine the move in some reasonable (to be defined) time.
So such a change from one interface to another is not a piece of cake at all.
@BaronVonChickenpants You might be right that it works as such. I have no idea how it works in detail in the chess.com interface.
However, I tried to play with the DGT board yesterday and today, and it is not reliably picking up moves. The voice extension also does not work again. I tried with two different boards and computers, no way.
Would you mind trying this? Somebody, in the meantime, improved the voice extension. Though it is barely used, I found this improvement to be working. But moves are not picked up reliably, though, so there is no way of playing with the board on chess.com now.

I haven't tried the board in some time, but will set it up and see if the voice thing still works. I did have one older laptop that the DGT interface just stopped working on at all.
The mystery solved now, keeping the users complaining for nearly one year, one must use the old interface to use the voice extension and DGT board. See this post, to use the DGT board with chess.com just start games using Play / Live Chess / Play (old interface). Do not use Play / + New Game / Play (new interface). The new interface does not work with the voice extension and the DGT board. Please check my post and shout for nobody informing any earlier.
If the board is out of sync and one makes a move on the board, chess.com accepts the board move (if a possible move for the actual position). But that is a problem, as in this situation, one has not the correct position on the board. It is better not to accept the board move when the position is out of sync and play an error sound.
Example:
White plays with the DGT board.
The game played is 1. Nf3 e5 2. g3 e4 3. Bg2 exf3, but White only realizes when too late.