If you don't want this to be "the usual political football", you might consider
1) Not making every other word "Obama", since he's not the topic.
2) Not making the thrust of every other paragraph "this is hypocrisy" when the topic is ostensibly "where best to spend the money".
Since you have done those, I'll take a moment to address some:
There is a difference between a subsidy and a loan. There is a difference between a bail-out and an investment. When you compare this to domestic subsidies, you are being unreasonable. This would better compare to the FRB and its role in the US economy. That's not something that Obama has criticized (making loans available for US companies), and that's the directly related activity.
The discussion over drilling is somewhat apples and oranges as well. I don't see any reason to believe that the Im-Ex bank has chosen this action based on increasing oil production. Rather it seems to be targeted at creating a market for American exports (the task of the Im-Ex bank) and this particular loan happens to be for a company looking to do off-shore drilling.
The Im-Ex loans out lots of money, and I'm sure there are any number of "green energy" projects as well, along with tons of non-energy projects. The short is "invest to make a market for US exports".
Would this money actually be better spent here? On what in particular. Is there a specific multi-national stable US company looking for loans or loan guarantees that you feel are not available? I'm worried that you are basing your argument on this assumption and that it may be entirely false.
Finally, and I say this as someone whose beaches would be impacted by offshore drilling: the issue of off-shore drilling off the US is only economic in the sense that it's negative impact on , for example, tourism in Florida is a factor.
If the reason that Exxon could not drill in the gulf was that it could not secure a loan, then your point would be valid. Since that's not the reason, it's apples-and-oranges.
I'll finish this with one quote that illustrates several of my points:
Yet he has no trouble committing $2,000,000,000 of our money for Brazil to drill off its own coast.
Did Obama personally push for this? I doubt it, so why do you keep mentioning him? Can you show that any money is actually committed? It looks like we are offering loan guarantees, so that's a straw-man. The commitment is intended to make a profit. Do you believe that the government making a profit (and thereby needing less tax-payer money to pay the bills) is a bad thing? Finally, the end focus is to get Brazil to buy US products. Do you think investing to let US companies sell their goods overseas is bad?
Yes, yes: you think that these guarantees somehow mean that some loan won't happen in the US. Can you point me at an example?