I think it's exactly as disruptive as any other messaging system.
I think if you're working on an open source project, then it follows that you probably support open source software, or better yet free software, and you could switch to using a free alternative to Slack, of which there are plenty. You could tweak them to be less "hostile", too.
I think the problem isn't the software, I think it's people (it's always people, isn't it?)
Personally I don't have a problem with these things because I don't look at them very often. I check my email when I reach a natural break or if I need to look something specific up - and in that case I don't pay attention to the unread count and open anything I don't need to at that instant.
Same with Slack, or IRC or whatever.
Slack can be good for technical conversations, and the fact that it is asynchronous really but sometimes it comes across as synchronous is a strength rather than a weakness. I'll get a reply eventually, when it's convenient for the other parties. That might be straight away, it might not. And that's ok.
I don't use the search very often because anything I need to know I tend to copy to a more appropriate place - code snippets go in a snippet manager or whatever, I update READMEs with instructions, that sort of thing.
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