Trans-Exclusionary Radical Feminists (TERFs), also known as Trans-Exclusionary Radicals (TERs) or Feminism-Appropriating Reactionary Transphobes (FARTs), are transphobes who justify their transphobia under the guise of feminism. TERFs are known for hatred of trans women particularly.
TERFs often prey on young, uneducated gay people (particularly lesbians) to indoctrinate them into their ideology. Because of this, there is a large age discrepancy in TERF groups. Older TERFs (usually around their 30s) have been kicked out of local real life LGBT+ spaces due to their transphobia, so they turn to the internet to spread their bigotry. They often target young (around 12-15) lesbians who likely do not have access to real life LGBT+ spaces, and are therefore less educated on LGBT issues and are easier to manipulate. To those not familiar with TERF ideology it can be difficult to spot it, as TERF mask their bigotry with the guise of feminism. They will often make statements about "men", if one did not know that person is a TERF one would not assume that statement actually meant trans women. By hiding what they're actually saying behind more innocuous statements, they can get people to agree with them and from there can indoctrinate them into their way of thinking.
TERFs' main doctrine is that trans people do not exist. They believe that trans women are actually men who are trying to invade women's spaces and men who fetishize womanhood and have "autogynephilia." They also believe that trans men are actually confused women with internalized misogyny. If they're attracted to women they think they're lesbian/bisexual with internalized lesbophobia/homophobia, and if they're attracted to men then they're a straight/bisexual woman who wants to pretend to be a gay man because they've seen too much yaoi.
Obsession with "Biology"
TERFs equate women with their genitals and believe that women are those with "natural-born" vaginas and uteri and, more recently, XX chromosomes. As such TERFs will frequently use symbols of a vagina or uterus to represent women. They also obsess over biological processes such as periods and the ability to give birth. They sometimes refer to cis women as "womben" (a combination of women and womb).
Similarly they sometimes use the word "womyn". This alternate spelling was originally meant as a way to avoid the suffix 'man'. However it was adopted by TERFs to mean cis women. TERFs also use the womyn-born-womyn (WBW) to mean "women raised as women", to exclude anyone assigned male at birth.
Prejudice Against AMAB People
TERFs believe that all men are inherently oppressive and cannot change this due to the way they enforce the patriarchy. Trans women, and anyone assigned male at birth are included in this outdated definition of "men." They believe that, because they were born and were raised as men, all AMABs do not understand what it is like to be a woman and do benefit from male privilege. They argue that all AMAB's experience sex-based privilege: that being perceived as a boy for a good chunk of their life means they didn't have to experience misogyny growing up. They also argue that they have the privilege of not experiencing the downsides of having an AFAB body, such as ever having to worry about being denied an abortion.
Views on Transmasculine People
As with many conversations on trans people, transmasculine people, such as transgender men and AFAB nonbinary people, are often left out of the conversation. When they are acknowledged, TERFs often brand them as gender non-conforming women with internalized misogyny or claim to support them because they believe all AFAB people are "female." They argue that because they're perceived as women-- either currently, or in the past-- they still experience misogyny and are therefore included in feminism.
It's worth mentioning that FTM TERFs exist, as well as FTMTF de-transitioners. The detransitioners often feel that they were allowed to transition too easily, and that medical professionals didn't bother digging deeply into the origins of their dysphoria and just presented transition as the only solution. Many of them have trauma related to being AFAB and hadn't realized at first that they wanted to transition to escape that. So they see young FTM individuals and mistakenly see themselves in them, and don't want them to make the same mistake they did. Many support transition as a last resort and simply want dysphoric AFAB individuals to look into other options first.
Biphobia is rampant in TERF groups. They often believe that relationships with men (and trans women), particularly sexual relationships, are oppressive and women who willingly form relationships with men, such as straight women or bisexual women are oppressing themselves due to societal pressure. As such many TERFs are lesbians and refuse to be romantically involved with bisexual women under the belief that they've been "tainted" by men.
TERF ideology often includes being against kinky sex, believing that dom/sub interactions, even between two women, mirror the oppressive relationship between men and women. Therefore TERF ideology asserted that the only "pure" form of sex is vanilla sex between two (strictly lesbian) cis women.
Many TERFs are also sex-worker exclusionary radical feminists or SWERFs.
They're also against porn for many reasons, such as normalizing violence against women and the women in the videos being abused on the job. Many TERFs are sex workers or former sex workers who speak out against the industry and talk about the abuse they faced within it.
Dislike of the Word TERF
Many TERFs dislike being called TERFs as the word blatantly calls out their transphobia. Many will try to claim that TERF is a slur. They often call themselves gender critical, radical feminists or radfems, which leaves out the trans-exclusionary part to hide their bigotry.
The TERF "pride flag" is based on a flag for the women's suffrage movement. It is often mistaken as the genderqueer pride flag due to its similar color scheme.