I think one of the best things about the bsd is that there are no real deadly sins. Dr Mosley seems to be quite a kind guru in that I have often heard him say that the odd bit of something will not harm. So the odd bit of chocolate, the odd bit of bread, etc, so long as it really is quite a rare occurrence. The important thing is not to view that little stray as an excuse to have a pity party and pull all the wheels off the wagon.
I’m no expert but I’d suggest there’s a couple of things you could look at to decide whether to have it or not. Do you have a blood sugar tester? If so, test your blood two hours after eating your rye bread and see if it raises your sugar level beyond what is acceptable. If it does, then you know there are good health reasons to avoid it, if it doesn’t then you can enjoy some when you want to. You will want to check the calorie count and make sure that you can make room for it in your 800 calories.
Even if you can’t make room for it, you may decide to keep it as a real treat every once in a while. I have just finished reading an article on this website about mindfully eating cake and drinking coffee so maybe you could substitute the cake for bread and eat it in a mindful way.