This fallacy has been debunked so many * times, it's getting tiresome. The only pressure applied to banks was pressure from their own greed. They wanted in on the MBS action, so they created their own CDOs from loans originated by non-banks like Countrywide. As entities like Countrywide are not regulated as banks, they weren't compelled by any law to originate loans from low-income homeowners, if that's this "pressure" that you're referring to. In fact, these loans were way more risky than the FHA loans that the GSEs originated and securitized,
However, around the time the * hit the fan, the GSEs did start lowering their origination standards--not because of some government mandate, but because they wanted to regain market share of the MBS market that they lost to the investment banks creating CDOs from portfolios of subprime loans. Again, greed is solely responsible. You have to remember that GSEs are NOT some sort of government agencies. They are true private sector companies that were traded on the NYSE.
"As entities like Countrywide are not regulated as banks."
Yea, which also means Countrywide wasn't regulated under Glass-Steagall or other laws in the first place, so I could use Countrywide's example to argue all of the deregulation that happened in the 90s can't be blamed for the subprime crisis either. Or Bear-Stearns', or Merill Lynch's, or other financial groups. We're talking about factors tangentially affecting the collapse here.
The mortgage-backed security market in the first place didn't exist because of greed, and lax lending standards were encouraged by the government in the 90s through legal measures. Countrywide and other financial companies weren't particularly greedy in following the lead of lending standards that were being done everywhere else. Maybe they should have known better, but that's a different issue than whether they were greedy.
As for GSEs, they have heavy government oversight and support and encouragement. Often their decisions are political, not financial. And while Republicans fought to deregulate the private market, they were also fighting to tighten regulations GSEs, which the federal government has special authority to do. Democrats were often doing the opposite. While Republicans like deregulation on the private market, they happen to like regulation of publicly sponsored entities.
Anyway, its hard to disentangle either the market side or the regulatory side from the end result, and blame one over the other.