Cape and dress colors?

Gorgeous. Its still pretty white to me.. bit depending on lighting . You should be good

Beautiful. Most ivory is close enough to white that no one can tell them apart.

There is no need to match. When you wear a red dress, do you only wear sweaters, coats, or capes of that same color red? There are many colors and textures of the white family that go together. Notoriously, bone white with a greyish undertone is awful with yellowish cream. But many of the shades are fine together. Look at whites designer rooms. Clothiers with expensive duds will tell you a white shirt, not a cream or ivory one should be worn with a cream or ivory jacket, as long as they are not extreme tints. This is an ad for very formal duds.

The guy is wearing 7 colors of whites/ ivory/ cream. Only one does not belong. The satin tie. The bride is a distinctly different shade, white against his ivory jacket. How it is supposed to be. Otherwise, seen from across a room, or in pictures on a bright day, or where there are dark colors nearby, the auto light meters of a camera would make 1 bright white blob of his clothes and hers. No details of either would show, and his arm would merge with her dress.
All of these shades will look a little different from shadows, and shifting shine on satins. ( say that twice!)But all are compatible. When your dress and cape are finished/ properly pressed, try them on. Of they look different, but nice, that is fine. You will not look like a ghostly blob in pic. The camera will sense the differences and amplify them a little so they are clearly different garments where they come together. If you are not sure, try an old costumer's trick: put the finest line of a different color at the meeting point of at least one of the places where different tones of a color come together. A 1/4 inch gold metallic braid, or narrow satin gold trim, sewn where the fur white meets the cape white. As the different thing, your eye will flick from one white to the gold to the ivory to a white, noticing that greater contrast, and not the finer one between the whites. Really. You can use a color besides gold, but gold braid or satin trim does not have dye to run when cleaned, like navy or other high contrast colors. Cameras have trouble with details when all whites match. No contrast to give things shape and form.

Most of the time people can't tell the difference. I think it'll be ok since your dress and cape are two different fabrics as well.

You really won't know unless you put the two materials side by side. Not all whites are the same, not all ivories are the same. Some whites are a lot softer and have slight warm undertones, and some are pretty stark with cool undertones. I've found that brands that make dresses for all different functions (such as Lulu's) will call a shade "white" and it may be a soft white color, whereas manufacturers that specialize in wedding dresses and offer the same dress in several different shades will usually have a much starker true white if "white" is one of the color options. If the white of your dress has neutral or warm undertones, it might look fine next to the ivory even if it's not the exact same color. Chances are if your dress came in a few different color options, such as white, ivory, champagne, oyster, blush, nude, etc and you picked out "white" then it's going to be pretty different from a typical ivory, but you just really have to compare them side by side to know.

I know when my husband was looking at dress shirts for his suit, trying to match my dress was difficult (especially since I didn't want him to actually see my dress, and he didn't have a swatch of sample fabric when he went suit shopping). I gave him a different dress I bought in a material that was "close enough" in color to compare. Some white shirts were way too bright, and men's ivory shirts tended to be a darker ivory (like the color of a manila folder, whereas most bridal ivory is a lot brighter). The shirt he ended up getting was brighter/whiter than my dress, but still a softer white so it didn't make my dress look dingy.

Looks awesome- there’s no need to worry. You’re going to rock that dress & cape!

I don't see an issue with the color difference.