Not even close to the same thing
Recognizing biological reality is not misgendering. There is no such thing as a "trans woman" or a "trans man."
One user on Twitter complained that people will correct you if you call a male dog a "she" (or vice versa) but if you correct someone "misgendering" trans people you are called a social justice warrior authoritarian and accused of advancing "compelled speech." (I am intentionally not linking to the user, because she is not the point.) But the comparison is deeply flawed because the situations are totally different.
If someone calls a male dog a female and is corrected, the person doing the correcting is pointing out a biological fact. The male dog is genetically and anatomically male. This is not an issue of feelings, ideology or compassion. This is simply pointing out an objective fact. If someone tells me I must refer to a "trans woman" as she/her, that person is not pointing out a fact. That person is telling me that I must deny an objective fact in order to protect someone's feelings or go along with moral convictions I do not share.
A "trans woman" is a man. He is genetically male with x/y chromosomes. He was born with a penis, testicles and a prostate - organs that women do not have. If he pays an unethical so-called "doctor" to mutilate his genitals and starts taking harmful hormone treatments, he is still biologically and genetically male. If you tell me that I must refer to a biological male as "she/her" then you are telling me I am required to lie.
If someone believes that he is not the "gender" that matches his biological sex, that person is having a break with reality. It is not helpful or loving to encourage and celebrate that delusion. It is hateful for the same reason that a father who refuses to discipline his children hates them. If you want the best for someone, you should want them to seek help to recognize biological reality and not embrace a delusion and a lie. "Transgender" people are victims of a cultural Left that is exploiting their pain and illness to attack all distinctions and further destroy the Christian value base that has built Western civilization.