They have now accepted concerns about the centuries-old St Patrick's College in Maynooth, Co Kildare, and have ordered a review.
An inquiry will look at the "appropriate use of the internet and social media" by trainee clergymen.
It comes weeks after the Catholic Archbishop of Dublin confirmed he was boycotting the seminary.
Dr Diarmuid Martin, one of the most senior Catholics in Ireland, said earlier this month he is sending student priests to Rome rather than Maynooth.
He said he made the decision some months ago because he was "somewhat unhappy" about "an atmosphere that was growing in Maynooth" exposed through anonymous accusations in letters and online blogs.
Dr Martin said allegations included "a gay culture, that students have been using an app called Grindr" which he said "would be fostering promiscuous sexuality".
Now the college trustees - four Archbishops and 13 senior Bishops - have met for crisis talks.
They acknowledged the controversy and the disquiet it has caused in the church in Ireland.
"The trustees share the concerns about the unhealthy atmosphere created by anonymous accusations together with some social media comments which can be speculative or even malicious," they said in a statement.
"Persons with specific concerns are encouraged to report them appropriately as soon as possible."
There had also been concerns about the way whistle-blowers had been treated. Reports suggested some men who reported the use of the app had been asked to leave the college.
The trustees have vowed to carry out a review of whistle-blowing policies and procedures and will demand college authorities review the use of the internet and social media.
Founded in 1795, Maynooth College was once the largest seminary in the world.
It was built to train 500 trainee Catholic priests every year, but numbers have nosedived to just over 40 for the coming year with a fall-off in vocations.
