Could installing mods to Beat Saber have negative consequences?

Besides the risks of installing anything from unknown sources online (not to say anything about this source in particular); it does not appear like you should expect any repercussions at this time.

Beat Saber is well aware of the modding community, and so far as not taken direct action against the community. Some new patches seem to break mod support; but even in that case it sounds as though the developers quickly added the ability to use previous builds, which allowed the old mods to still function.

There was some concern from the community that modding would cause issues in the future, because the EULA was updated to include wording that concerned some users. This seems like it is a non-issue based on the twitter response from the developers.

@MrSpamsel 'Spamsel': "Hi @BeatSaber @Split82 @BeatGamesStudio is there any official statement about EULA 4.2.5. "edit, merge, distribute, translate, reverse engineer, [...]" prohibiting the mods and the modding community? Some people are going crazy about it #BeatSaber"

@Split82 'Jan “Split” Ilavsky': "EULA is here to protect us, not to go after anyone. We do plan to support mods and modders more in the future. Nothing to go crazy about."

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Unless the developers are lying, the only consequences of installing mods should be due to the effects of what you are installing on your computer; which I cannot vouch for (though presumably the mods with a lot of community support are as safe as most community projects online).

Installing mods for Beat Saber is allowed, and mostly encouraged by the community.

Beat Saber mods are an important part of the game, and as well as being condoned by the makers, my guess is that it is a core part of that value that the designed into the game - being able to do more and create more.

The only thing I would say is that there are a lot of good guides about Beat Saber mods out there, and IMO this guide on Beat Saber mods is longer and more informative.