Factionalism appears within the trans community as well.

transfeminine versus transmasculine

Outside of the transgender community, transmasculine identities are preferred over transfeminine identities. (for instance, see the statistics regarding LGBT murders)

This dynamic expresses itself in transgender spaces sometimes as well.

binary versus non-binary

Some transgender people are ideologically opposed to the gender binary, and are pretty adamant about their opposition (genderqueer, gender fluid, etc). But some transgender people do things that appear to actively support it (transsexuals). This can create tension.

transsexual separatism

Some transsexuals seem themselves as completely separate from anyone else on the transgender spectrum.

drag queens/kings

Unlike other trans folks, they do not have the strenuous insistence that they strongly identify with their trans gender-expression.

stratification

"Transgender" is an umbrella term can cover many different forms of gender-variant behavior. Some that are included:

Because there is such a wide range of behavior, there are many different labels that people self-apply, and sometimes label use can be contentious for an individual ("no! I'm not a X! I prefer Y instead! Don't call me X!"), even when a particular label is seen as generally acceptable for others to use.

But don't get distracted by labels. Even if we removed all terminology, there are still clear differences in behavior, discrimination that a particular subgroup faces, and lived daily experiences of people in that subgroup.

As such, some wish to clearly distinguish themselves from others under the transgender umbrella, and may have animosity towards other subgroups.