The use of the word "tankie" these days is so over-used it has become synonymous with "left of the DNC." I've even seen Anarchists described as "tankies," it's getting ridiculous. Still, the word "tankie" is most often used by liberals against Marxists, though they won't admit to having an anti-Marxist bias, mostly because they think they agree with Marx generally but are unfamiliar with Marxist analysis.
Really, more people need to read theory before having an opinion on it to avoid speaking past each other. I wrote an introductory reading list for Marxism-Leninism if anyone wants to get a better understanding of Marxism.