I'm going to respond to that, in two sections:
The database is a tool used with the intent of reporting those who, agreeably, have posted vile and disgusting remarks about Charlie Kirk's assassination in order to get them fired from their job. The morality of that intent is what's in question, in reference to the Biblical command and presupposition that work is necessary for one to be worthy of eating. Getting people fired, which will affect their household income and budgets (especially in a negative way in this current weak economy), for speech which hasn't murdered a victim is very extreme. There are other ways of dealing with hateful or vulgar speech besides using it to prevent others from providing for their dependents, which can, itself, lead to death.
Though I agree that employers can fire employees at their discretion and prerogative, it seems a bit draconian to actively archive expressions of speech which are detestable, with the intent to share those expressions of speech with a given employer, in order to take away the person's means of income, without which the employer may have never known about those expressions. Yes, we all will give an account before God for our words, but we also need to have some measure of grace and wisdom in dealing with those who spew vile things online, understanding that the central problem is their heart, not their place of employment.