advice How to know specifically that a domain is being blacklisted or not?

Bodis have a tool which can be used to check blacklisted status of 1000 domains/day

There are countless tools you can use online. Search on Google

likewise said:

How to know specifically that a domain is being blacklisted or not?

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you have to be more specific... what blacklist???

Utilize this free Domain Blacklist Check to check whether your area is on a Real Time This RBL Database Lookup demonstrates you explicit boycotts and their names,