Assuming:
If a character would gain the same proficiency from two different sources, he or she can choose a different proficiency of the same kind (skill or tool) instead. (PBR, p. 36; PHB, p. 126)
A Tabaxi Rogue with the Criminal Background has the following skill proficiencies:
- Racial (Tabaxi): Stealth and Perception
- Class (Rogue): Four from Acrobatics, Athletics, Deception, Insight, Intimidation, Investigation, Perception, Performance, Persuasion, Sleight of Hand, and Stealth.
- Background (Criminal): Deception and Stealth.
With this in mind I'm looking at a build with the following proficiencies:
- Stealth (racial)
- Perception (racial)
- Acrobatics (class)
- Intimidation (class)
- Persuasion (class)
- Investigation (class)
- Deception (background)
- Sleight of Hand (background/Dex substitute for Stealth)
Is this valid by RAW?
Best Answer
Yes: those proficiency choices are supported by RAW
From the Basic Rules, and the same section in the PHB:
Thus you can pick the other background skill proficiency to make up for an overlap/duplicate. Your 8 skill proficiencies, as you presented, is supported by RAW.
Additional point on customization
You can customize a background per the PHB/RAW
Customizing a Background
I have found, from both sides of the table, that a collobrative workup of the background/back story between DM and player makes for a good fit between the player and the campaign.