It's impossible to have the "Tireless Precision" bonus of a Vedalken apply to thieves tools as a rogue, when you should be able to do this. The issue is that it forces you to choose the proficiency as a rogue, when you should be able to choose another if you already have the proficiency from being a Vedalken. 

Same issue, 2021

This seems more like an oversight with the system of the game itself and not DndBeyond. Because you gain proficiency from being a rogue without a choice of a different option, you can't swap it out the same way you would be able to if you had a choice on the proficiency or not. Because of this, you wouldn't be able to choose it as a gained proficiency with Tireless Precision because you already have proficiency with it. That being said, I don't believe there is any difference within the display of DndBeyond for the Tireless Precision proficiency aside from actually telling you what it is. You would probably be okay with just choosing a different proficiency and then treating the additional D4 roll to your thieves' tools instead. 

At least that is how I would get around it within DndBeyond and how I would treat it as a DM.

Technically, you should choose your race before choosing your class. Dnd beyond doesn't let you do this however.

D&D Beyond does allow you to choose race before class, or build your character in almost any order.

The character builder lists the same order of recommended steps as found in the basic rules:

1. Race
2. Class
3. Abilities
4. Description
5. Equipment

However, you can totally jump to abilities first, then description, then race and finally class, or whatever order you want.

If you want to set tireless precision to thieves tools, leave the option unselected when you choose your race, then select your class as normal, then go back and select thieves tools.

Alternatively you can go straight to class first and set that, then pick your race.

you still should be able to choose thieves tool's for tireless precision first, even if it doesn't give you a replacement proficiency for choosing rogue.

Necro'ing this because its still an issue. The Vedalken feature doesn't say "any tool unless Thieves Tools if you are also a Rogue"

Well, I was going to make a bug report, but as this exists already I guess the correct method is to add to it as it's an unsolved issue?
Same issue as with rogue Vedalken but with artificer, can't apply the 1d4 bonus to checks to a proficiency that you get from your class.

Again, you definitely can add the d4 if you choose. you'd just need to make a note to do it and remember the proficiency you've chosen for it. The issue is a limitation within the way dnd beyond is built as a way to not allow people to have proficiency with the same ability twice and since class doesn't dive you the option (sometimes) and the race does have a choice it makes the racial feature make you choose a different option.

With a very literal interpretation of RAW, you wouldn't be able to apply it to that proficiency since you don't get via that skill anyway because you can't have proficiency with the same ability twice. Though I would certainly not rule it this way.