Unless the late Mr. Crooks jotted down a manifesto or otherwise is discovered to reveal his motive, we're not going to know, and are only able to guess at why he shot at Trump. Let me repeat that: We can only guess and will never know unless we get really lucky.
(One of my favorite details of a shooter incident was Adam Lanza's favorite video game obsession, Dance Dance Revolution since it was still a common opinion that video games trained rampage killers. Tastes in video games and music are about as useful as needing to impress Jodie Foster, or reread The Catcher In the Rye. You may be a lover, Adam, but you ain't no dancer.)
Crooks' choice of weapon (an AR-15–style rifle ) indicates a weapon of convenience. He didn't have the time or means to get something that was more suited to the task. This fits more the profile of a radicalized civilian than a trained operative.
When Al-Qaeda wanted to attack a target (or CIA, or IRA, or any other active group trying to influence a theater of conflict) they'd look at the suicide demographics. What young people are killing themselves in high numbers. Then, in the internet age, it's a matter of finding people who are self-radicalized, who want to express their outrage violently. And then its a matter of grooming that person (in this case very much the way predators groom children) to see the target of interest as the site / VIP / venue of the terror action. The rampage killer / saboteur / terrorist never knows who he's working for or what his cause is, only that by suicide bombing at this site, he'll be heard and known.
Is this to say Crooks was pointed at killing Trump by CIA? Not at all. Trump is an easy viable target, and there are plenty of reasons to be pissed off at him that make sense. But the reason that Crooks had to express his discontent violently has likely very little to do with Trump directly, and whether he's left-wing and wants to stop the US' descent into one-party autocracy, or he's far-right wing and thinks Trump is selling out isn't why he's shooting.
There are however, droves of pre-radicalized war boys in the US, silver paint in hand wanting an opportunity to be witnessed all shiny and chrome into Valhalla. A lot of them can be seen in the alt-right, the incels, the MGTOWs the alpha-male wannabes who have been entirely disregarded since they were teens without explanation or education, and are expected by society to either magically turn into high-paid salarymen, or suffer as losers in a single-occupant dwelling in a dead-end job where they're overworked and underpaid. This lot tends to be a bit dissatisfied with their lot in life.
I'm not saying Crooks is one of these guys, only that it's a big circle on the Venn-diagram, and not a difficult target to fall into. This circle not only has a higher-than-average male suicide rate (which is already high in the general population) but also is where pro-trump militants and the transnational white power movement gets its recruits. And they tend to register Republican.
Again, we don't know, only this might inform our guesses.
A registered party member is just someone who voted in the primary.
The Democratic primaries in my area had a bunch of uncontested seats or I was comfortable with all the candidates, so I registered Republican to vote against Trump.
I'm a registered Republican, but I am not a supporter of the GOP.
Continued information coming out about him confirm he was an active and proud conservative. Quoted students confirmed this and the like-minded alt-right group of kids he hung out with.
Consider this. As this was his first presidential election to vote in, registering Democrat meant voting in a meaningless primary, so registering Republican would be a strategic choice to vote against Trump as a nominee.
Is this the case? We don't know yet, but voter registration for a 20 year old doesn't infer much
He registered as a Republican in 2021, and voted in the 2022 election, so it wasn't for a strategic vote against Trump, unless he was thinking ahead by several years.
So I have two (conflicting) thoughts regarding people as right wing.
Firstly, here in the States, right-wing encompasses a lot of spectrum, from the extreme reactionary / accelerationist folks that are keen to replicate the worst of the atrocities of the German Reich, to those who are neoliberal / neoconservative, and believes in a multi-faceted economy, a pluralist, secular culture and the use of military adventurism to secure American interests abroad when diplomacy and trade relations fail to bring those about.
Crooks could come from anywhere in this gamut, whether he is (what I suspect) an extremist glad to serve the new American order as a militant or an operative on the field, or someone who is Republican because they identify as [R] but still wish to see the US as a place where democracy and government by the people prevails. (It isn't, with our democratic features tightly constrained, but the rival party prevents one party from taking absolute power.)
Secondly, when it comes to Republican intellegentsia, there's a tendency to want their party to be less extreme than they have become, as we've seen with those Republicans like Brad Raffensburger who is not willing to cheat or collaborate with Republican officials to bend the system to secure an election victory, but who still believes in the anti-poor, anti-labor, pro-prison, pro-police Republican policies that laid the rails to our current situation on the precipice of autocratic takeover. We have a lot of people who knowingly voted in Reagan, George H. W. Bush, George W. Bush and Donald J. Trump, and kept voting Republicans down-ballot, aware that the policies they preferred would eventually drive the US to the kind of general precarity and discontent that leads to systemic breakdown and autocratic rule.
But that's not where Crooks is, as much as we like to imagine our operatives are playing 5D chess, whether they're allies or enemies. Essentially, Crooks did as most terrorists and rampage killers did, and committed angry suicide, with as little actual planning as he could manage.
But that could change if Mr. Wrench chatted with him on line for twenty hours over the course of four weeks convincing him to take a pot-shot at Trump, or if he's done a lot of reading of political theory and came to such a conclusion on his own. But until that evidence comes up, I think he was just acting out of pure rage based on personal circumstances.