my experience telling normies i like avant-garde music has been generally positive, but by this i mean describing the music to them rather than making them listen to it. many people have seemed somewhat curious and fascinated, while others just move the conversation to something else. i haven't had anyone say something rude or sceptical of my sincerity when i've said that i like experimental improvised music, which is something i've said to dozens of people irl. some people will respond positively by connecting what i'm describing to something they like and *think* is "experimental," but actually isn't. like after i gave a presentation on onkyokei to a room full of people, one of them started asking me if i know about some japanese neo-psychedelia indie band he liked.
my "strategy" for "converting" people is just to get them to make a rym account and then leave them to explore and read about more music on their own. curious people naturally will. it does probably start with something like the velvet underground long before anything without melody -- you need to first start thinking about music as an artform in which sounds, harmonies, and concepts are explored rather than simply a medium revolving around creating catchy melodies or "bangers." people who already like Actual Good Music (e.g., the velvet underground) are, in my experience, almost always interested in listening to *noisier* and/or more complex music, but music without melody is a different thing entirely. the same people just become bored and say they don't "get it." i think you either feel captivated and fascinated by truly avant-garde music or you don't. i don't think there's really a way of easing into it -- "pleasant" drone and ambient seems like it'd just teach them to listen to experimental music as background music. maybe noise music could be the bridge (since it isn't pleasant), but like i said earlier, i don't really micromanage or tinker with people's taste like this. i just try to get them exposed to a much wider range/variety of music in album form.
the people with a seething hatred of avantmusic are usually spergs who already really like some other genre of music (usually metal, sometimes prog rock and classical) and feel the need to gatekeep the music fandom from people they don't want to see advancing a way of approaching music that wouldn't be compatible with ranking the things they like as objectively superior. i think casuals are much more likely to seethe at abstract visual art because it is often bourgeois and they associate it with rich snobs (or LIBTARDS) and a world they feel excluded from. avantmusic is something much lesser known and will more often be seen as a quaint curiousity, especially if you're talking about an underground scene.