I'm Polish, and with Slovaks, Belarussians, Ukrainians it's more than 60%. With Czechs it's maybe 50% cause of their pronounciation, with Russians it's maybe 40-50%, because they have weird word roots.
Maybe it's because I'm vaguely aware of the phonetic changes between east and west Slavic languages (ić - it, ska - skaja, etc), because I've heard some Russian and Ukrainian on street markets in 90s.
Haven't had much experience with other Slavic speakers, but Serbian sounds quite close to western Slavic from the songs I've heard.
But, yes, with English being the de facto standard, these more localized attempts are becoming redundant - you want to know English anyway because you want to talk to more people, and once you know it, you might as well use it to talk even to people whose languages are related to yours.