1) You can be a neocon and an evangelical. Neocon are defined by their hawkish foreign, you can still believe in Religious Liberty and be a hawk. Proven by Ted Cruz, who won the 2016 Iowa caucus (won because of his support from evangelicals)and is a foreign policy hawk.
2) Bill Clinton's sympathy vote is dramatically overstated because Democrats are portrayed as weak on Foreign Policy , so he could be potrayed as to have been the cause. Just imagine Fox News if 911 happened under Gore.....
3) Terror attacks have profound effects on Republicans. Remember that in July 2002 Bush had a 99 percent approval rating from Republicans. Despite signing the patriot act which goes against the idea of small government. So I think the reaction from Republicans would have been more grand in the 90s during the peak of evangelicalism.
4) Pat Robertson would just have to tone down the anti-Isreal rhetoric. He would be unpalatable to the establishment but I think he wins with the base especially if there's a crowded field.
5) The 2 things would be probably enough to win the geneal but if not, just have Bill Clintons sex scandals come earlier. Then you would have a 2000 effect where people vote for Robertson because of his "Moral Strength "
1) Yes, you can, but what's relevant is that Al Qaeda is very clearly a foreign threat, and not something endemic to American society. Robertson and his ilk would be rather alone in attributing the attack to domestic societal rot. It would make them seem disconnection from reality, and honestly disrespectful to the dead if they tried arguing that the attack was reason for America to focus more on religious virtue to prevent future incidents.
2) Just as well Fox didn't exist until October of 1996, then. Otherwise, the rally around the flag effect doesn't seem to discriminate historically. And any weakness of Clinton's on the foreign front is harmful to Robertson, more below.
3) You shouldn't overestimate how much Republican voters (or leaders, for that matter) really care about small government. Government spending has risen continuously since the immediate post-WW2 aftermath, and yet no Republican President has been held accountable for their part in the expansion. I agree that a terror attack would have profound effects, and help Robertson...if he was already President. But he isn't here, so we finally get to the real heart of the problem.
4) Yeah, no, it wouldn't be that simple. This isn't a stray remark here or there we're talking about. In 1991, five years before our election, he wrote a book in which he described a shadow conspiracy that secretly controls the world. Including all the usual suspects, among them
Jewish bankers. That is not something he can casually disavow, and Bob Dole and others would hammer him relentlessly on it. Now, there is some good news for him here: in the event of an early War on Terror, Pat Buchanan's isolationism would go nowhere. But that's the only good news. The bad news is that when Buchanan scared Dole in Iowa and New Hampshire IOTL, the rest of the Party promptly rallied behind Dole. That suggests that the more successful Robertson is, the less crowded the field will become.
And Dole is also very attractive on his own: a Senate leader for years, and a WW2 vet with an inspiring life story. The perfect foil to draft dodging Clinton in a foreign policy election. The Democrats did much the same thing with Kerry in 2004, after all. In the meantime, Robertson's Antisemitism would make him seem like an enemy of Israel...right when we're getting more involved in the Middle East and need all the help we can get. Throw in the GOP's shift towards Hegelian idealism after the fall of the Berlin Wall, and Robertson's Huntington-esque chauvinism would be dangerously off-brand. Remember, the Bush Administration strongly disavowed the notion that America was at war with Islam.
There's no Fox or Twitter to carry his words, AIPAC would be up in arms against him, and the whole Party would be willing to denounce him, whereas they didn't endorse Trump in 2016, but otherwise treated him with kid gloves during the primaries. Robertson would be eaten alive.
5) One of those things you haven't made a case for beyond "It's what Anthony Kennedy secretly wanted," and the other would benefit Robertson's primary rivals more than him. And Bill had sex scandals throughout his Administration. There's a reason the eventual Evangelical President we got was softer and less overbearing about his virtue. The extremists offend too many people to take the spotlight.
Honestly, I don't think you quite appreciate just how far outside the mainstream Robertson's brand of chiding, authoritarian fundamentalism was, or how figures like him aren't really supposed to occupy the spotlight. They're niche figures, who rely on alliances with more inclusive bodies like the Republican Party to wield real power instead of just getting marginalized. You need something like Rumsfeldia to make an environment where he could actually win through.