I will try to answer your questions. Note that I am a Theist, and my religious beliefs are derived from Christianity. Note also that I resigned my post as church elder earlier this year because the people I served with just would not "get it". Thus, my answers are based on my understanding of 'Fundie' doctrine and traditions.
Could someone please explain to me why they can't "let up" for even a short period of time?
Because they are required to "
always" present their views to the world...
"Therefore, my dear brothers, stand firm. Let nothing move you. Always give yourselves fully to the work of the LORD, because you know that your labor in the LORD is not in vain." -- 1 COR 15:58 (NIV)
Why can't they see the harm their words create?
Because they stubbornly adhere to their doctrine, rather than follow God's ordinances of compassion and mercy...
"You warned them to return to your law, but they became arrogant and disobeyed your commands. They sinned against your ordinances, by which a man will live if he obeys them. Stubbornly they turned their backs on you, became stiff-necked and refused to listen." -- NEH 9:29 (NIV)
And...
"But they did not listen to me or pay attention. They were stiff-necked and did more evil than their forefathers." -- JER 7:26 (NIV)
...and are these religious people completely beyond redemption?
No ... I was once like them. It has been a steady process of 'redemption' over the past few years, and I still have a long way to go. There are others like me who are more interested in being Christ-like than in trying to force any particular version of Christianity "down everybody's throats".
Is there any more hope left that they could see the error of their ways?
Yes, but not all of them, and not right away. There will always be 'fundies' who seek to destroy in body or spirit (or both) anyone who is not already one of their number.
Has Obama and Hilary's message done any good?
Not much. At least, not among those fundies who believe that Ms. Clinton and Mr. Obama are irrevocably lost and therefore tools of Satan. Most fundies that I know have already decided that any statement released by the current administration is either a package of lies, or a call to sin. Either way, the fundies won't listen -- they just won't "get it". To them, any lie, any act of violence, and any breach of common decency they commit is okay, as long as they do it in "The Name of the Lord".
I voted for Geezer McCain and Caribou Barbie. Yet I cringe whenever I hear a fundie criticize Mr. Obama, mainly because their criticisms are largely unfounded. It's a tough job, every president makes mistakes, and not every president enjoys the full cooperation of Congress and the support of the people.
If I may suggest to the LGBT 'community' (however it defines itself), try advocating for yourselves and each other first. That is, build yourselves up individually, insofar as education and economic success are concerned, and help each other do the same for themselves. Earn your way into positions of authority, where you may exercise greater influence in corporate hiring and political assignments. Work for the overall good of your neighborhood, without regard to any cosmetic factor or subtle hostility -- do good works, and let others see that you care about other people's needs, and not just your own. If someone starts hassling you, walk away. Bullies are not important, no matter how 'holy' they may be.
Fundies will always see you as a threat, even when they smile, shake your hand, and welcome you to their congregations. "Once a sinner, always a sinner" is the unspoken rule, and anyone who has ever been openly 'sinning' (by their definitions) is and always will be a 'sinner'.