Don't ever give your Google Mail password to another company. Even if they "encrypt" it on the wire, you can never be sure they're not storing it insecurely on the back end. Please take this from someone who spends his days beating up other people's applications: everyone screws up something.
I always wonder "what's up with that"? Is it that the particular assets don't lend themselves to injection, or an assumption that items delivered from a server under their control can't or won't be intercepted? If the latter, particularly once the traffic hits an unsecured wireless segment, I'd be inclined to say all bets are off.
EDIT: Nit: HN linkified the bare protocol designations.
I probably should have made this very clear: While the lack of encryption is maddening, the very worst part is that Tumblr isn't performing this data pull properly (and Google does provide a proper and relatively safe mechanism for doing what they're doing--it's used by Facebook, LinkedIn and anyone else with a need, API key and good conscience).