The Sherlock star is one of the first celebrities to have been confirmed as a contestant for the 2023 series of the BBC dance show.
Her Strictly signing sparked a row on social media among some users who were offended by a comment the actor made earlier this years about a baby sensory show featuring a drag act.
Abbington, 51, said in a video on Instagram: "I've said stupid things in the past but it's what you do after them that's important. I'm not transphobic and I love women...
"So I'm sorry if my tweet about drag shows made you feel like you can't watch Strictly, I'm genuinely sorry."
The actor - who has two children with her ex-partner of 16 years The Office star Martin Freeman - revealed she had deleted her Twitter account but felt she must address comments being made about her on the platform.
She explained: "Apparently I'm trending on Twitter. I'm not on Twitter anymore. I left voluntarily because I don't like it over there anymore.
"I'm trending because people are going to boycott Strictly and I think it's because of a tweet I made back in March regarding a drag show."
She went on: "I'm not transphobic, I'm not a transphobic person, I'm a firm supporter of the legitimate trans community, I always have been. I think they have been infiltrated by some people who want to cause damage and want to cause trouble, and pit people off of each other and cause as much harm as possible.
"But I would support any trans person who is feeling persecuted or not listened to, or not seen, of course I would. I'm not a nasty person.'
"I support the trans community, I also support women's rights and I support the importance of women within society, and I think those two are being really pitted against each other."
Abbington added: "So I'm sorry if you feel like you need to boycott Strictly for a tweet I made about a drag show but I don't think 12-year-olds should be doing overly-sexualised drag acts. That's my personal opinion and I'm not pushing it on anyone else. It upsets me when I see kids feeling like they have to do that.
"But I didn't associate it with the trans community nor would I. I'm an ally of the LGBT community and I'm an ally of women's rights and I'm an ally of kids being kids, and I'm an ally of live and let live."
In March 2023 she tweeted "I lost quite a few followers for saying that a semi-naked man in thigh high boots dancing in a highly sexualised way shouldn't be performing in front of babies and it tells me everything I need to know about where society is heading. How do you not agree with me on this?"
The post was seen 2.2million times and received nearly 2,000 retweets.
In response to being called a TERF (Trans-Exclusionary Radical Feminist) she then tweeted: "I never mentioned the trans community! How on earth is my post transphobic. I'm saying you do not perform that kind of act in front of BABIES. It's abhorrent."
Addressing the re-surfaced post in her Instagram video Abbington said: "Now, I need to make this very clear. I love drag... My son played Jamie in Everyone's Taking About Jamie and he was a wonderful drag queen, he was wonderful in it.
"But my tweet back in March was regarding a 12-year-old who was doing it in front of adults and it just upset me because I saw a kid, a little kid, a 12-year-old doing something very over-sexualised and I didn't think it was right."
Abbington, is engaged to escapologist Jonathan Goodwin, 43. The stunt magician — who is known for appearing on Britain's Got Talent in 2019 — nearly died after falling 30 feet between two burning cars and missing a safety airbag below when a stunt rehearsal went wrong, and is now paralysed from the waist down.
Other celebrities confirmed for the new series of Strictly so far include journalist Krishnan Guru-Murthy and 78-year-old newsreader Angela Rippon.
Watch: Jonathan Goodwin told Amanda Abbington she could leave him after he was paralysed