You would really need to go to your local unit of government and look up (or have them do so) the deed which transferred ownership to the land conservancy to check and see if there were any use restrictions or mandates associated with the conveyance. There may also be a conservation easement document related to this which may either be publicly recorded or on file at the land conservancy. Since land trusts/conservancies typically have 501(c)3 IRS tax designation any management or use restriction which is contrary to the stated desires to the donor is potentially a major issue for them. If all else fails, I would open a discussion with the land conservancy staff, or Board, to see what their policy was based on and encourage further discussion.
Another issue that we, as sportsmen, should be raising is the issue of habitat management on conservancy lands. Too many are stopping all timber stand management in favor of Old Growth which is a de facto way of impacting the availability of game species. Again, if the donor had a management preference, that's fine. If, however, these decisions are being made solely by a staff and board of directors, then we should be engaging in these discussions. Frankly, they should be supporting a land management strategy which supports a the full range of wildlife species.
On behalf of all of us who support land protection but oppose the loss of hunting opportunities, thanks for raising this issue.