Actually I'd say trans women both suffer from and exhibit misogyny.
They suffer from misogyny in that patriarchy devalues, rejects and (perhaps as a psychological result of the first two) often actively hates female humans. This then transfers onto anything that is female-associated or coded.
IMO both homophobia and "Transphobia" - the latter not of course the entirely reasonable statement that trans people are not in fact members of the opposite sex so we shouldn't pretend they are, but the real thing, the base emotional reaction of fear/hated of trans presenting people, especially men presenting as women, because their cross gender presentation is perceived as weird or wrong - are both simply different expressions of underlying sexism and misogyny.
The patriarchal subconcious (which both men and women have as a consequence of living in a patriarchy) believes male trumps female and therefore has the right to power and privilege that female does not, so reacts very strongly to a deliberately feminine male as a traitor to men.
As an analogy, in the 50s and 60s many white musicians playing blues were subject to abuse for playing "black" music. To that degree, despite not being black and so never facing the lifetime of racism that black musicians faced as an unescapable consequence of the immutable colour of their skin, they nevertheless were attacked and devalued because what they did offended racist values.
And yet, while recognising the above, it is ultimately undeniable that to believe in transgender identies one must first believe that there are mental aspects to of being "a woman" or "a man" which are the primary differences between the sexes not just consequences of ones life experiences of being one sex rather than the other. So primary indeed that one can be "really" the other sex based on ones mind alone.
And that also ultimately rests on the patriarchal constructs of the masculine and the feminine mind.
So while one can understand and accomodate the reality of transmisogyny within Feminist analys, ultimately Feminist analysis has to reject the primary existence of trans identies, understanding them as a phenomenon within patriarchy not a challenge from outside it.