I'd be totally accepting of friendly, 'we come in peace' aliens once that was proven they were friendly without a doubt.
Honestly, to me, the real problems would probably come from two areas:
Well, I guess the one way they could prove it is by doing what they said....mmet with everyone or no one....and not do anything that would be seen as invading. Funny how people would have a hard time taking them at their word while believing humans would be capable of being so honest and virtous in the "Is star trek possible" thread. (I don't buy that for a second about humans, just so you know.)
I'd assume that the aliens would have enough sense to take safeguards from espionage, and if they have technology that can get from their planet to here I don't think we'd be able to actually do espionage on them in the first place. They'd have to be a few hundred years ahead of us in tech at least.
But you're right, religious extremists would go nuts. We'd probably have to barricade off all of the red states for awhile. I think just as many people would riot against fearful religious zealots. Why trun down a huge step in science and knowledge about the universe because it makes a bunch of yahoos doubt their beliefs?
Religious extremists would be obvious, the ones who would declare the aliens 'the spawn from Hell' and such things. They'd do everything in their power to demonize the aliens and use scare tactics to keep people on their side, and they'd be the ones who'd want the aliens to leave.
Whether or not you agree with Carl Sagan, the book/movie Contact is what I feel, a good example at how it could very realistically happen. Maybe it is a bit more on the extreme end of the spectrum, but I majorly doubt that really really religious types would be...nice about it, and many people would be scared and unsure about their place in the universe, and thus flock to such groups due to those emotions.
Espionage. This would come from two groups:
A. Big business who would see their various power-bases starting to break down, and they'd do everything in their power to sabotage the aliens.
B. Other governments. Namely they would try and 'friendly up' to the aliens, in order to gain an advantage over other governments, and possibly try to out-right steal technology for their country and their country only.
If aliens did exist, and appeared today, I'd hope that maybe any governments who KNEW this would come clean about it.
If I were the aliens I would make sure the entire world could get the message so no one government could lie or try to twist the truth. How effective that would be, I don't know. Heck, I'd even make usre the formula for "renewable clean energy" was put on the internet just to screw over the oil tycoons. Of course, I'm assuming they've been monitoring us for awhile.
Of course I meant for this scenario to be as I said...the aliens are sincerely friendly with no hidden agenda. (well, if they were evil, realistically we couldn't stop them anyway. Its like if the Borg suddenly showed up tomorrow. Its not like we could do anything but be assimilated.)
...and what if they did want something, but it was something really simple? Like they said "we want tomatoes. On our world tomatoes are powerful medicine. Could you spare a few tomato plants...we can grow them on our own planet but we'd like a few tons of the plants and some seeds too. In exchange we'll help you out with the fuel problem.".
(I just got an image of the religious extremists burning piles of spaghetti sauce)