TERF, or Trans Exclusionary Radical Feminist, is a type of second wave feminist who believes that trans women (male to female transgenders) are men and not women. They feel trans women have not and cannot fully experience what being a woman is like and therefore should not identify as women as TERFs feel it would amplify, confuse or downplay the societal issues that people born with vagina's face. They believe this because they think a man, even if he feels like a woman, isn't treated like women are growing up and therefore cannot fully experience womanhood.
Gender Abolitionist TERFs
Some, but not all, TERFs consider gender to be inherently oppressive and consider trans people to be gender essentialists. Even though these TERFs often find gender oppressive, they do not believe one can simply choose to switch genders, but rather only society can raise people as certain genders from birth.
Conflict with Modern, Third Wave Feminism
Third wave feminists on the other hand believe that all gender identities are as valid as the person who creates them wants them to be. Although TERFs sometimes dislike the movement for different reasons than US conservatives, both conservatives and TERFs agree that people who call themselves 'trans' can only be the gender they were assigned at birth in the modern world.