Usually clients have some option to do it but the steps might be different based on what client you're using.
Right now I'm on Voyager for example and if let's say I wanted to block your instance I could click your profile and click the options. One of the options on that screen is "View Instance" and from there I have the option to block the instance.
There's also post filters but I know a lot less about setting those up. But iirc one of the things you can filter posts by is the instance the post comes from.
The actual type of play on words is called paraprosdokian. Where the in this case punchline is surprising in a way that makes you reinterpret the setup.
In this case "I wanna be supportive but," is kind of priming the reader to expect they're gonna say some transphobic shit then you read "fucking Mildred?" and those expectations are subverted by the actual point being essentially "Why you taking names from 2000's obituaries?"
To my knowledge there's not like a widespread name for this as like a comedic genre because it's just one of the basic ways you can structure a joke. I've seen some comics call it a swerve or an anti-climax but nothing widespread.