There are two kinds of Republicans: 1) the kind that tolerated and used Trump to overturn Roe and achieve related agenda items 2) the kind that used Roe and related agenda items to get Trump power.
Trump really is a racist and autocrat, but obviously he is no Christian fundamentalist. When he first started running he knew nothing about abortion (other than how to pay for one). Early in his campaign he was asked if he really thought women should be out in prison for getting an abortion and he went full Trump on why they should, not realizing that savvy Republicans had long ago learned to duck that punch, and say they wanted to outlaw abortion but not out women in jail. It was a two day story before they taught him how to answer it.
Dobbs will hurt Republicans in upcoming elections, there is no doubt about that. A majority of American voters wanted to retain Roe, at least in some form. Trump wanted to keep Roe as an issue. There is more doubt over how much it will hurt Republicans- I doubt enough to decide who will control Congress (but, maybe).
More interesting to me, Will achieving their goal lead Christian fanatics to abandon Trump and switch over to someone a little more of their own?
And yes, there is a third kind of Republican, almost extinct, that wonders what the fuck happened to their party.