Aer Lingus use US Preclearance in Dublin, so you arrive in the US as basically a domestic passenger. No need to re-collect your bags, no need to go through immigration/customs, and no need to clear security unless the layout of the airport requires it. Your inbound flight will land in Terminal G, and Alaska uses Terminal 2 (D gates). The good news is that as of last year those two terminals are connected airside, so you can walk from G to D without having to clear security. Depending on the exact gates, it's a maybe 10-15 minute walk at most.

So yes, 1 hour 45 mins is more than enough. If you do happen to mis-connect (eg, if your DUB-SFO flight is delayed) then Alaska will move you to a later flight.

Without pre-clearance this connection would be possible but tight. With it, it's a breeze!