one has to differentiate between - lets say the Core ... and the BHG.
the BHG is a loose guild of professional hunters. - but the major point is that it provides a network of contracts - yet every hunter works either alone or in a small team. - a bounty hunter can also take a contract that was not given by the BHG network - the bhg network just makes things easier - which gives a bhg ( in RP ) the edge over the common freelancer / mercenary - who relies on his own network of contact.
the core however is - as montezuma said ... not the bhg. - they don t really take bounties - and act as a military. - they are also not vanilla - hence need to become a part of the vanilla balance still.
a problem that the whole BHG faction suffers from is the lack of infrastructure. - if we leave out guard systems, which are often quite ooRP, cause they are build on request rather than possibilities ( in general, not in particular here ) - they have 2 bases. - rostock.... and dabadoru.
for a siriuswide faction - that is also looking to expand into a newly found house - thats very little.
BHG depend on police bases in house space..... and freeports in the edgeworlds... unless they get more allies. - this is not a one sided dependency though.... bhg ( in vanilla ) provide mutual protection for the bases they are staged on ( meaning freeports ).
all in all - gallia perverts many of the sirius ideals. - unlawfuls fighting the lawfuls in gallia are indeed those that welcome lawfuls in sirius the most. - while the lawfuls in gallia are the villains in sirius. ( even up to another quality than kusari / bretonia - or liberty / rheinland )
the bhg - the hunters - should easily be able to take contracts by the gallic unlawfuls....
why? - the whole "rule" is based on a character guideline.
BHG take lawful contracts - cause they decided to be a lawful force. - lawful by sirius standards, mind. - and that is the point. - lawful does not equal lawful.... a policeman may be sworn to keep up the law in his country - and in his country that means ... he protects the innocent and hunts down those that wish to hurt the innocent.
however - in another country the law might say "you must hunt down the innocent and praise the villains" - the same policeman would not hold up that law, cause it goes against all he considers "lawful".
lawful - is an ideal rather than the letter of the law in that case. - a house of lawfuls whos only purpose is to invade and kill is not lawful by the BHG standards. so allying with the unlawfuls ( unlawful from the pov of the lawfuls in that house ) is an option... but ONLY if the methods of those unlawfuls match the ideal of a lawful by sirius standards.
so a terrorist might not be a possible ally, even if he fights another villain.
and as mentioned before - if the bhg cannot count on bases in these regions - they cannot operate there anyway. - so they must find a someone that matches their idea of "lawful" - that is also willing to provide shelter. - after all, they cannot fly from rostock to the gallic regions all the time.
the core again is a military section. - they may have their own agenda and motives. - but they do also depend heavily on what bases they can use. - currently they have one single base in delta - which is about as far from gallia as it can get. the core however is more suited to fight for a higher ideal - and for their own good of course, then the common BHG, - simply cause they can make a greater impact.
considering that the bhg core and the order have maintained a balance in the omicrons - its hard to believe that they can fight a two frontier war though.... cause the problematic thing about balance is that even a tiny bit can upset it. - so if they retreat from the omicrons - the conflict there might be lost.... either forever or they d need a huge efford to regain what they lost again. - unless they have made more allies in the region.