Catholics United Education Fund planned to protest Tuesday outside the Knights' New Haven headquarters.
The liberal advocacy group, which claims 45,000 members, says the Knights spent more than $600,000 opposing same-sex marriage in the last election cycle.
The effort drives younger Catholics away from the faith and the Knights should focus on serving the poor and vulnerable, the group said.
"As Catholics who love the church, many of whom like myself have dedicated my life to the church, are saddened that the faith is increasingly aligned with a far right reactionary political agenda," said James Salt, executive director of Catholics United.
The Knights, which provides life insurance and is the largest lay Catholic organization in the world, said it supports Catholic social teaching, including on moral issues.
The group says its first concern has always been charity, and over the past decade has donated more than $1.4 billion and 664 million hours to charitable causes.
Catholics United, citing a report last month from a coalition of Catholics who support gay rights, said the Knights donated more than $600,000 this year for ballot initiatives in Maine, Maryland, Minnesota and Washington state.
Voters in Washington, Maryland and Maine approved gay marriage earlier this month, while Minnesota voters rejected a proposed constitutional amendment to ban same-sex marriage.
The Catholic Church supported anti-gay marriage campaigns in those states.
The Knights have spent more than $6 million since 2005 opposing same-sex marriage, according to the report cited by Catholics United.