are people also offended by 'heterosexual'?
The analogy between 'cis' and 'hetero' only works very superficially.
For 'heterosexual' and 'homosexual' to both have meaning, they need to both be subsets of a larger category. In this case, that is 'sexual orientation': the sex of the individuals with whom someone wishes to form intimate emotional and sexual relationships. Hence, both homo- and heterosexual individuals have a sexual orientation. Yes, some are attracted to both men and women but no-one is arguing that the very notion of a sexual orientation itself is nonsense as it manifestly isn't.
Following the same logic, for 'ciswoman' and 'transwoman' to both be meaningful, they have to both be subsets of the same larger category 'woman'. But unlike the concept of 'sexual orientation', which is quite easy to define, the problem with conceptualising 'cis'- and 'trans' women is that no-one seems to be able to explain with any clarity what properties of this supposedly clear super-category 'woman' are common to both 'cis' and 'trans' variety women. Clearly it cannot be biological properties such as a vagina, ovaries or breasts as this would exclude transwomen. But if these are not the properties that define 'woman', what exactly are these elusive properties? Is it a set of conventions around behaviour and clothing? Hair, makeup, a set of personality traits? Who gets to decide these? What are they? No-one can decide or agree, except to fall back on a strange mixture of regressive stereotypes about 'femininity' and a woolly notion that 'it's how you feel inside' and only an individual can decide for themselves. And if it's something that individuals can only define for themselves it's effectively meaningless as there is no objective measure for my or your self-perception.
So what, you ask? Well, basically, by using the concept 'cis' to make biological sex a subset of a larger, vaguer category called 'women', you make that category either meaningless or a mess of exactly the stereotypes that women have been challenging for centuries. And you also make it nigh-on impossible to discuss the very specific ways that people with female biology are at a disadvantage in numerous contexts within society. Because, thanks to the term 'cis' having moved the goalposts for what 'woman' means, people with female biology (formerly known as 'women') no longer have a collective noun that describes them. Which means they cannot easily speak about their experience, conduct political activism related to issues they face or otherwise address the numerous challenges still faced - specifically - by people whose biology is female. None of this is to say there is no other group that faces challenges, but I struggle to think of another group whose very language to self-describe, self-define and organise politically to address those challenges is so unthinkingly under threat, and in the name of liberalism and progress too.
I hope that explains in a bit more detail why people object to the conceptual framework imposed by the word 'cis'. It has profound political implications and simply is not comparable to naming a norm such as white or heterosexual people.