The following userscript is based on the fantastic comment from @Makyen

// ==UserScript==
// @name        Ignore user in transcript
// @match       *://chat.stackexchange.com/transcript/*
// @grant       none
// @run-at      document-start
// ==/UserScript==

document.documentElement.insertAdjacentHTML('beforeend', '<style type="text/css">.monologue.user-249772 {display:none;}</style>');

(replace 249772 with the ID of the user you'd like to ignore)

The following userscript is based on the fantastic comment from @Makyen (therefore making this a community wiki answer)

// ==UserScript==
// @name        Ignore user in transcript
// @match       *://chat.stackexchange.com/transcript/*
// @grant       none
// @run-at      document-start
// ==/UserScript==

document.documentElement.insertAdjacentHTML('beforeend', '<style type="text/css">.monologue.user-249772 {display:none;}</style>');

(replace 249772 with the ID of the user you'd like to ignore)

The following userscript is based on the idea fantastic comment from @Makyen

// ==UserScript==
// @name        Ignore user in transcript
// @match       *://chat.stackexchange.com/transcript/*
// @grant       none
// @run-at      document-start
// ==/UserScript==

document.documentElement.insertAdjacentHTML('beforeend', '<style type="text/css">.monologue.user-249772 {display:none;}</style>');

(replace 249772 with the ID of the user you'd like to ignore)

The following userscript is based on the fantastic comment from @Makyen

// ==UserScript==
// @name        Ignore user in transcript
// @match       *://chat.stackexchange.com/transcript/*
// @grant       none
// @run-at      document-start
// ==/UserScript==

document.documentElement.insertAdjacentHTML('beforeend', '<style type="text/css">.monologue.user-249772 {display:none;}</style>');

(replace 249772 with the ID of the user you'd like to ignore)