Solution

To properly constraint these paths, the word "core" in the path should be replaced with the component name that the RXAUI core was generated with in /sources_1/ip/core_name/synth/core_name.xdc.  This file is read only, but can be edited outside of the Vivado GUI. In the following constraints "core" should be replaced with the name of the core as shown below with the text "core_name":


set_false_path -from [get_cells -hierarchical -filter {NAME =~ */mgt_powerdown_falling_reg}] -to [get_cells -hierarchical -filter {NAME =~ */gt0_core_name_gt_wrapper_i/gtrxreset_seq_i/gtrxreset_s_reg}]
set_false_path -from [get_cells -hierarchical -filter {NAME =~ */sync_counter_reg[*]}] -to [get_cells -hierarchical -filter {NAME =~ */gt0_core_name_gt_wrapper_i/gtrxreset_seq_i/gtrxreset_s_reg}]
set_false_path -from [get_cells -hierarchical -filter {NAME =~ */mgt_powerdown_falling_reg}] -to [get_cells -hierarchical -filter {NAME =~ */gt0_core_name_gt_wrapper_i/gtrxreset_seq_i/DRP_OP_DONE_reg}]
set_false_path -from [get_cells -hierarchical -filter {NAME =~ */mgt_powerdown_falling_reg}] -to [get_cells -hierarchical -filter {NAME =~ */gt1_core_name_gt_wrapper_i/gtrxreset_seq_i/DRP_OP_DONE_reg}]
set_false_path -from [get_cells -hierarchical -filter {NAME =~ */sync_counter_reg[*]}] -to [get_cells -hierarchical -filter {NAME =~ */gt0_core_name_gt_wrapper_i/gtrxreset_seq_i/DRP_OP_DONE_reg}]
set_false_path -from [get_cells -hierarchical -filter {NAME =~ */sync_counter_reg[*]}] -to [get_cells -hierarchical -filter {NAME =~ */gt1_core_name_gt_wrapper_i/gtrxreset_seq_i/DRP_OP_DONE_reg}]
set_false_path -from [get_cells -hierarchical -filter {NAME =~ *management_1/reset_reg_reg}] -to [get_cells -hierarchical -filter {NAME =~ */gt0_core_name_gt_wrapper_i/gtrxreset_seq_i/gtrxreset_s_reg}]
set_false_path -from [get_cells -hierarchical -filter {NAME =~ */mgt_loopback_falling_reg}] -to [get_cells -hierarchical -filter {NAME =~ */gt0_core_name_gt_wrapper_i/gtrxreset_seq_i/gtrxreset_s_reg}]
set_false_path -from [get_cells -hierarchical -filter {NAME =~ *management_1/reset_reg_reg}] -to [get_cells -hierarchical -filter {NAME =~ */gt0_core_name_gt_wrapper_i/gtrxreset_seq_i/DRP_OP_DONE_reg}]
set_false_path -from [get_cells -hierarchical -filter {NAME =~ *management_1/reset_reg_reg}] -to [get_cells -hierarchical -filter {NAME =~ */gt1_core_name_gt_wrapper_i/gtrxreset_seq_i/DRP_OP_DONE_reg}]
set_false_path -from [get_cells -hierarchical -filter {NAME =~ */mgt_loopback_falling_reg}] -to [get_cells -hierarchical -filter {NAME =~ */gt0_core_name_gt_wrapper_i/gtrxreset_seq_i/DRP_OP_DONE_reg}]
set_false_path -from [get_cells -hierarchical -filter {NAME =~ */mgt_loopback_falling_reg}] -to [get_cells -hierarchical -filter {NAME =~ */gt1_core_name_gt_wrapper_i/gtrxreset_seq_i/DRP_OP_DONE_reg}]

These constraints could also be added to the design top level to constrain the paths, although the critical warning will still be reported if the core specific xdc is not edited.