Google's issue tracker has an open issue revolving around possibly giving users the ability to choose custom emoji fonts in the future, and Google has responded to the issue by saying that it has been pushed on to a future release if it will happen, but it's possible. Many users in the issue are rallying for the option to use custom emoji in general, but many share a sentiment that they want to be able to use Google's old "blob" emoji, which began to be phased out with Android 7.0 (Nougat), and are completely gone as of Android 8.0 (Oreo). There is no official word as yet on how the feature may manifest, but many comments are gravitating toward implementing a system to change your device's emoji font in much the same way that the normal system font can be changed.
The blob emoji that many users are talking about in this issue tracker thread were recently issued a fond farewell in the form of a cheesy love letter chock full of pop culture references. As of Android Oreo, the blobs have been replaced by defined, humanlike emoji that somewhat accurately represent Android's user base. The new emoji are meant to be diverse enough to represent most or all users, while also representing a wide range of emotions and actions. They are meant to be consistent with the emoji found in other services and ecosystems. Customizable Bitmoji and emoji stickers for Allo dynamically crafted by AI from a user's face are there to fill in the gaps, though they cannot be used quite as widely as the new regular emoji.
Google's blob emoji came about back in 2013, and were the default for Android system applications and Google apps for a long time. The set of blob emoji available grew over time, but issues with consistency in the art style and emotion of the emoji began to emerge. After a while, Google announced that these issues had ballooned over time and become enough of a problem that it warranted starting over. To that end, Google announced that the blobs would be making their exit.