Despite what the media makes it sound like, mainstream America isn't going anti gun and doesn't care that much about cutting emissions and all that. That isn't why the Republican Party is declining. By the way, you ask about agreeing to "some gun control" as if there is no gun control or as if the Republican Party is against any type of gun control at all when there's lots of gun control and laws, there's just no gun ban.

Part of the problem is the religious element, yeah social conservatism, their position on gay marriage and abortion is a huge turn off, especially with younger generations. So it'll be hard to take them serious because of this. But this will work itself out over time after the older generations die off.

The real issues that drive people to vote for either party comes down to money. The economy and how people perceive republicans and conservatism.
Even though Republicans don't cut spending or welfare when they gain power, the perception is that they will, and the democrats can easily pander to the poor with promising to expand welfare benefits. The more people subsidized by the government, the bigger loyal and permanent voting base they will continue to have. More government spending means less resources going towards private investment and more towards politically driven projects. WhicH further harms the economy and now more people become dependent on the state.
Trust me. Tweaking a few things on gun control and environmental talk will change NOTHING.

There's no fixing the Republican Party. The house of cards has to collapse first.