We must understand
the different position based on their different roles to see a good
picture.
Your
bf
He is your bf and of course, he wouldn't like competition. He may
not mind competition but when a zero chance competitor gets
annoying and affected his gf, the bf will get irritated and pissed.
He will request you to ignore him completely and avoid
contacts
Your
Mum
Your mum, being your mum, would want to protect her daughter. In
her heart, if your current relationship has already been
established and there for a good period, your mum may see him as a
potential son-in-law or my good daughters' good bf. In just case,
she would want you to avoid because she fear complication for good
or for ill. Standing on her POV, she feel it's unneccessary to
contact that guy.
You
As a friend for six years, you feel that giving him the contact has
no problem since you have already made known to him that he stand
no chance - your conscience is clear. Whether you give or not,
doesn't matter so much to you. Just that, even he may have liking
for you, he is still a friend.
Verdict? 
As long as you know what you truely wants - give or don't give
doesn't matter at all. It's only about your preference. You give,
you also won't like him. You don't give, you also won't like him.
The verdict has already been set years ago. So, it is really up to
you.
P.S: Yes, people around you are concerned and paranoid. But you
make the choice. In my opinion, it doesn't matter.
Cheers
