Probably not much of an impact to alter the overall results of the 1976 election, as (if I recall correctly) Jimmy Carter ran as a pro-life candidate whereas Gerald Ford was ambivalent regarding the issue of abortion rights. Down the line however, if abortion remained a state issue, it is likely that the Democrats would have retained slightly more support among white Catholics and Evangelical Protestants in the South and Midwest. More Democratic support amongst those groups, in turn, might have been enough to alter the results of several close Presidential elections such as 2000, 2004, and maybe 2016.
2016 would most definitely flip before 2004 in any sort of swing of results across multiple elections.
Kerry needed a 2.2% swing to win the 2004 tipping point state of Ohio.
Clinton needed a 0.8% swing to win the 2016 tipping point state of Wisconsin.
(both of the above numbers were rounded up to the nearest tenth of a percent in that direction)
