Hermit, Outlander, Sage, etc. all get a language trait from choosing that background. However, it's not made clear whether these languages stack with the languages that races provide, or replace them.

For example, a character playing as an Elf will get the following languages:

Languages. You can speak, read, and write Common and Elvish.

Alternatively, in the Outlander background:

Languages: One of your choice

Say a player was playing an Elf with an Outlander background. Which takes precedence? Racial over background, background over racial, or do they stack and happily coexist in a trilingual level 1 elf?

A background gives you extra languages, on top of the ones you know from your race

As per the basic rules (emphasis mine):

A background gives your character a background feature (a general benefit) and proficiency in two skills, and it might also give you additional languages or proficiency with certain kinds of tools.

When you choose a background, you add the features it grants to your existing traits. Your Outlander Elf should know three languages - common, Elvish, and another of your choice.

Resolve the Issue by Customizing your Background

In the scenario where a Background gives you a language that has already been provided by your Race/Class, you should be able to just swap it out directly. The Player's Handbook contains a section specifically dedicated to customizing Backgrounds, which you can use:

Customizing a Background

You might want to tweak some of the features of a background so it better fits your character or the campaign setting. To customize a background, you can replace one feature with any other one, choose any two skills, and choose a total of two tool proficiencies or languages from the sample backgrounds. You can either use the equipment package from your background or spend coin on gear as described in chapter 5. (If you spend coin, you can't also take the equipment package suggested for your class.) Finally, choose two personality traits, one ideal, one bond, and one flaw.

If you can't find a feature that matches your desired background, work with your DM to create one.

As far as I'm aware, this is considered a core part of the rules, and isn't just a Variant rule. Moreover, this is Adventurer's League compatible, so it's very unlikely your DM would refuse to permit this.