Yes, that is a good point, yet intra-tradition tensions of that kind are unavoidable, and probably to some extent productive. I do wonder though in all sincerity whether there is anything to be gained by one tradition critiquing another. Can such critiquing ever be fully detached from proselytization? Does it improve anyone's practice and help them learn more about their own tradition, or does it simply lead to agitation and fertile soil for Wrong Speech? I tend to get along well with people from other Buddhist traditions, but we usually don't go about critiquing each other's tradition... merely explain and ask questions about what life is like on our own sides of the fence, so that we can understand each other better.
"Do not force others, including children, by any means whatsoever, to adopt your views, whether by authority, threat, money, propaganda, or even education." - Ven. Thich Nhat Hanh
"The uprooting of identity is seen by the noble ones as pleasurable; but this contradicts what the whole world sees." (Snp 3.12)
"To argue with a person who has renounced the use of reason is like administering medicine to the dead" - Thomas Paine