So this may sound like a "why would you want to do that?" question, but the game world in which we are playing doesn't have a single "Common" language (it actually has several).  Part of the story involves a cultural clash, which the language barrier is very much a part of.

Currently, we list both Common and the local common language, but we would very much like to be able to remove Common from the list.   

Short of homebrewing every race...is there a way to do this (and to add our own languages)?

You can add custom languages to character sheets and just ignore common.

I think there is some internal debate about adding custom languages with homebrew because it takes work to add a feature that essentially already exists.

It’s more than simply ignoring Common.   What about campaigns where elves speak Qyenyan (Sp?)?  Where a player wants their character to never have been exposed to the human world?

Sorry, but DDB is not a cheap tool, and the response “suck it up” (which is not exactly what you are saying, I know) isn’t really a good one. Heck, even if I could clone a race and change the languages there, that would be a start.

I think you're misunderstanding, they're not saying "suck it up", they're saying "here's a work around until they hopefully implement this feature". If you're in a campaign where your character speaks only a certain, non-common language, what's on your sheet won't affect that, it just serves as a reminder should you need to look at it.

And I'd disagree about DDB being "not a cheap tool"; you can use all of the (finished) tools for free with the SRD, including homebrew. It's a very cheap (free) tool.

So maybe I missed it...but I haven't seen anything which said they were considering it.   Just a few fans of the product (myself included) posting about the product.  If there's a spot where they are posting ideas they are/aren't considering, please point me in that direction, because I would love to keep on top of that.

And hopefully, you didn't stop reading after "suck it up" but I immediately indicated that I knew that wasn't what DxJxC was saying.   "Just ignore Common" wasn't really a helpful comment since I had already indicated that was what we were doing.

So I'm going to assume that there is no way to create your own languages or to create clones of races which leverage other languages in D&D Beyond.

I still don't think that we need to make languages a part of homebrew, but I will at least concede that being able to hide/remove features/languages/skills from the character sheet is just as important as being able to add custom ones.