Carla Malony, who was secretary of the GOP’s Beaver County branch, apologised for the series of posts she made on the social network last year.
Although it is unclear exactly when the comments were made, they appeared to be in reaction to players kneeling in protest as the national anthem played before NFL games.
In one post, Ms Malony described American footballers taking part in the gesture to protest cases of police brutality in the US as “over paid ignorant blacks”, suggesting they should “go to Africa”.
When another Facebook user commented: “Go Steelers,” in reference to the Pittsburgh Steelers NFL franchise, the GOP activist launched into another racially-charged tirade.
“Steelers are now just as bad as the rest of the over paid baboons. You respect your flag, country and our national atnthem (sic),” she wrote.
“Stop watching, or going to a game and paying for over priced food, water and tickets. Lets see how the baboons get paid when white people stop paying their salaries.”
The Beaver County Republican Committee said in a statement that it had accepted Ms Maloney's resignations from both of her roles in the party and denounced her comments.
“The views expressed in her posts are abhorrent and have no place in reasonable public discourse,” the committee said.
The NFL national anthem protests first began in 2016, when then-San Francisco 49ers quarterback Colin Kaepernick took a knee to highlight police violence against minority groups and racial inequalities in America.
Since then, hundreds of players have refused to observe the anthem at American football games and in a variety of other US sports.
The protests have drawn the ire of president Donald Trump, who last year called on NFL franchise owners to fire players who refused to stand during the national anthem.
From the beginning of the 2018 NFL season, due to start on Thursday, players will be required by league rules to observe the anthem on the field or stay in the dressing room.
In her resignation statement, Ms Malony apologised for her remarks about the protests, which she said had been “in poor taste.”
“I apologise for my distasteful, inappropriate and insensitive social media posts,” she added.
“Those that know me know that I come from a diverse family that represents modern America.
“I know my posts and comments were disrespectful to not only the people that I love, but families across the country.
“I know I am a better person than this and, as I step away from these public positions, I will work to show everyone who I truly am.”