SDLP leader Claire Hanna said that the education minister was showing "no empathy" to young people who are going into school "uncomfortable with themselves" and the "struggles and challenges" that they are facing.
Speaking at a press conference at Stormont, Hanna added that "at all times in school the welfare and the mental wellbeing of young people has to be at the core of the things we are doing.
"We'll be marking minister Givan against that".
Alliance education spokesperson Michelle Guy said Givan's decision on the guidance had "created a vacuum that is not helpful for anyone".
The Lagan Valley assembly member also described it as a "disgraceful distraction".
"On a day in which we're pulling the education minister into the chamber to answer for his ongoing failure to ensure appropriate provision for SEN students, the timing of this announcement is a clear attempt to divert attention from such a crucial issue," she said.
The Northern Ireland Teachers' Council (NITC) said Paul Givan's decision to remove the guidance "ignores the practical and pastoral needs of transgender and gender-questioning pupils".
A spokesperson for the NITC also said the withdrawal of the guidance will "create confusion and leave schools without the necessary framework to support these pupils effectively".
"We stand in solidarity with our trans colleagues and will fight to make sure that every workplace is one where difference is respected".
The guidance advised teachers to be "sensitive to the needs of transgender pupils, as well as to the needs of other pupils" when making decisions about the use of toilets and changing rooms.
"Where requested, staff should give a transgender pupil access to toilets which match their gender identity, unless there is good reason not to do so," the EA guidance had stated.
The guidance had also said that teachers and school staff did not have "unlimited right to freedom of expression" regarding their views on transgender people.
Teachers were advised that they should respect a transgender pupil's wishes with regard to what name they were called.
Givan's decision on the guidance also comes just days after it was announced the author of the landmark Cass report - which carried out a review of gender identity services in England - is to review Northern Ireland's gender services.
Health Minister Mike Nesbitt said Dr Hilary Cass had agreed to his request, and is expected to visit Northern Ireland with a team in November.