Yes,I think It's possible,but I don't know exactly how.
You can try this(should work,but I've never tried it):
Go to Freelancer\DATA\UNIVERSE\SYSTEMS and in system where your station is
and cnahge it's rep.
Some kind of example:
[Object
nickname = Li01_01 <-----------your base name here
ids_name = 196766
pos = -33270, 0, -33039
rotate = 0, -10, -10
ambient_color = 255, 0, 0
Archetype = planet_earthgrncld_4000
ids_info = 65759
spin = 0, 0.001000, 0
atmosphere_range = 4200
burn_color = 160, 222, 245
base = Li01_01_Base
reputation = li_p_grp <-----------Change to fc_uk_grp
visit = 1

Now go to Freelancer\DATA\MISSIONS/empathy.ini,find there
[RepChangeEffects}
group = fc_uk_grp
event = object_destruction, -0.030000 <---------cnange -0.030000 to 0
event = random_mission_success, 0.136300 <---------cnange 0.136300 to 0
event = random_mission_failure, -0.045000 <---------cnange -0.045000 to 0
event = random_mission_abortion, -0.067500 <---------cnange -0.067500 to 0
empathy_rate = li_n_grp, 0
empathy_rate = li_lsf_grp, 0
empathy_rate = li_p_grp, 0
empathy_rate = br_n_grp, 0
empathy_rate = br_p_grp, 0
empathy_rate = ku_n_grp, 0
empathy_rate = ku_p_grp, 0
empathy_rate = rh_n_grp, 0
empathy_rate = rh_p_grp, 0
empathy_rate = co_shi_grp, 0
empathy_rate = co_khc_grp, 0
empathy_rate = co_kt_grp, 0
empathy_rate = br_m_grp, 0
empathy_rate = co_me_grp, 0
empathy_rate = co_be_grp, 0
empathy_rate = co_rs_grp, 0
empathy_rate = co_vr_grp, 0
empathy_rate = co_ni_grp, 0
empathy_rate = rh_m_grp, 0
empathy_rate = co_ti_grp, 0
empathy_rate = co_ic_grp, 0
empathy_rate = co_ss_grp, 0
empathy_rate = co_hsp_grp, 0
empathy_rate = co_alg_grp, 0
empathy_rate = co_os_grp, 0
empathy_rate = co_nws_grp, 0
empathy_rate = fc_c_grp, 0
empathy_rate = fc_ou_grp, 0
empathy_rate = fc_rh_grp, 0
empathy_rate = fc_bd_grp, 0
empathy_rate = fc_j_grp, 0
empathy_rate = fc_h_grp, 0
empathy_rate = fc_m_grp, 0
empathy_rate = fc_x_grp, 0
empathy_rate = fc_b_grp, 0
empathy_rate = fc_g_grp, 0
empathy_rate = fc_lh_grp, 0
empathy_rate = fc_u_grp, 0
empathy_rate = fc_gc_grp, 0
empathy_rate = fc_lwb_grp, 0
empathy_rate = fc_fa_grp, 0
empathy_rate = fc_lr_grp, 0
empathy_rate = fc_or_grp, 0
empathy_rate = gd_gm_grp, 0
empathy_rate = fc_n_grp, 0
empathy_rate = fc_ln_grp, 0
empathy_rate = fc_kn_grp, 0
empathy_rate = fc_rn_grp, 0
empathy_rate = fc_ouk_grp, 0
empathy_rate = fc_q_grp, 0
empathy_rate = fc_f_grp, 0
empathy_rate = gd_im_grp, 0
empathy_rate = gd_z_grp, 0.100000 <---------cnange 0.100000 to 0
empathy_rate = gd_bh_grp, 0

Launch Freelancer.
Play.

Station would still get angered if I torped it as the changes you did are only to your rep and not to the bases hostility.

The station does not get hostile if you have a ,1 reputation to the station
(ie. station has li_n_grp rep, then you need a house = li_n_grp, 1 entry in your charfile)