According to the standard account of the thrift crisis it didn't have much if anything to do with money laundering. Even Wikipedia, which has a longer article on the topic doesn't mention guns, drugs, or money laundering being a factor. So, I'd chalk that quote you gave to yellow journalism (or the book version thereof).
That's not to say that even higher profile banks don't sometimes get involved with laundering money from drug trafficking etc.; see the more recent case of HSBC. In general, complying with anti-money-laundering provisions is more difficult/costly for the smaller financial institutions, which doesn't necessarily mean they have lower compliance than larger institutions. I couldn't find any study about that during the era you mention, but with respect to the Patriot Act provisions in that area, a study found that despite the higher cost they incurred smaller institutions didn't comply less than the bigger ones.
The US has progressively tightened anti-money laundering legislation, but I see no evidence that e.g. the 1988 bill was motivated by thrifts in any way (rather than by the war on drugs in general). You can read/search the hearings before the Baking Committee. I see no mention of thrifts in there, but several mentions of the war on drugs.
There is one book that quotes a press article of the time as saying:
Lawmakers routinely denounce 'S&L Kingpins' with the vehemence once reserved for drug lords or organized crime chieftains [...]
So maybe that's how some "crossing of the wires" happened. The phrase "S&L Kingpins" definitely produces quite a few hits in the press of the time. And an article on law actions in the context of the S&L crisis mentions:
Additionally, in 1990 Congress adopted a new criminal provision patterned on the "drug kingpin statute" to deal with the most serious
offenders. The new law makes it a crime to operate a "continuing financial crimes enterprise." In essence, the statute applies to anyone who
organizes, manages or supervises at least four other individuals in carrying out a series of banking violations in which $5 million or more in gross
receipts is amassed within a two-year period. The penalty for so-called
"S&L kingpins" ranges from ten years' to life imprisonment.
But it makes no mention of actual drug trafficker being involved.