The reaction would be far less. Islam is outside most American's experience, so they're afraid of it. Right-wing ideas are not, so they're viewed much less fearfully. The truth is that, since 9/11, right-wing terrorism has claimed three times as many lives as Islamic terror IOTL, but we have all these wars and surveillance programs to "deal with" the latter, but nothing comparable for the former.
Even a right-wing 9/11 wouldn't change this fundamental dynamic.
I'm not sure that would work in a 9/11 context (I agree with your general point vis-a-vis the perception of right wing terrorism and Islam)
9/11 is just such a huge out of context thing it has the ability to redefine things on its own. Now with radical Islamic terrorism it didn't have to redefine things too far (the US/West was already pretty damn anti it after all and all the collateral stuff that goes with that), but I think you will see a national wide reclassification of right wing terrorism if 9/11 is caused by it.
One of the things is that even though there are right wing extremest groups in the US right wing extremists terrorist acts tend to get put on the shoulders of individuals, now some of that is due to the narrative we often use to mitigate it but also because internal US security / law enforcement have recently generally done their best* to head off organised terrorist groups doing joined up terrorist campaigns on US soil.
Even T.McVeigh while obviously part of larger extremest right wing scene was basically able to pull off the Oklahoma city bombing with only the direct help of a mate and shit load of ammonium nitrate and a rental truck.
9/11 is not that, it requires teams, planing, training and organisation. I.e. it going to be really hard to sell the "lone impressionable nut tragedy, what can you do" narrative.
Another point, if thsi 9/11 goes off like the OTL one that means a right wing extremest group with at least 19-20 actors willing to deliberately suicide attack, that will also change the narrative about brown people terrorism and white people driven to extreme action.
So I think you will see:
1) a massively scaled up FBI programme of going after established right wing groups and preventing them from being established (and post Oklahoma there had already been serious action against them)
2). While some of the points the right wing extremists make wont be completely verboten from mainstream political discourse they will have to be much more careful in skirting that line and staying mainstream.
3). Policing of the internet will come in hard and faster, and i suspect incitement to violence/terrorist acts will be more applied against the far right than it was OTL
*Trumpo telling them to redirect elsewhere will have repercussions