Belfast need to avoid wearing orange/green?

I was just there last summer and although things have changed a lot in the last 20 years, I would still stay away from those colours. Wear a different jacket that day

After a ski trip in the Norwegian mountains we returned to Oslo in time for the St. Patrick's Day parade. I was wearing my orange mountain jacket and was subjected to some good natured jeers from the parade participants. But Norwegians, Irish or not, are a pretty good natured bunch and Oslo may not be representative of Belfast.

I really wouldn't pay it a second thought. Wear your jacket, you'll be fine.

While I agree that it's unlikely that anyone will notice or care, It would be prudent to check with your host (B&B, hotel, whatever) and get their advice once you're there - especially if your visit will be during the "marching season" in NI (google it to see what it's all about).
And I'd avoid any of the Orange parades, particularly on or around July 12th, no matter what your attire may be.

Wearing a green raincoat in NI will attract zero attention. Wearing a green raincoat whilst watching an Orange march will also attract zero attention.

Those who may be looking to cause trouble know who they're looking to cause trouble with, the OP in her green raincoat will not be one of them.

The point is that the prudent traveler will inquire locally before venturing into unfamiliar situations where passions may be running high.

Several years ago we happened to be in Belfast during the week leading up to the July 12th celebrations. One morning at breakfast I noticed that there was a march scheduled for later that day and my wife and I thought that it might be something fun to do ... a bit of local color. Long story short: when I asked the concierge at the place we were staying how best to get out to the venue where the parade was to be held he basically (but firmly) suggested that we steer clear of it. I believe he said something along the lines of "you never know what might happen at one of those things." Didn't think much of it at the time but followed his advice and gave it a miss. Next day's paper reported that at the conclusion of the march a scuffle broke out and that 10 or 15 policemen were injured by flying rocks as they tried to seperate the factions and restore order. Apparently some bystanders sustained minor injuries as well. Had it not been for advice of that particular local gentleman it's likely we'd have found ourselves in the middle of all that.
So ... that's what I mean by inquiring locally about current conditions, ie someone who physically lives in the city and who can thus best advise regarding potential trouble spots to be avoided. Belfast is a terrific city - we found it to be very safe and very tourist friendly. That said, there are places and situations (as is the case in any large city) that are best avoided absent local knowledge.

Robert's antidote does have relevance to whether to wear a green or orange raincoat. The March on July 12th or otherwise know as Orangeman's Day is the "Protestant" marchers celebration of William of Orange's victory over Catholic King James. I believe he was saying, you never know how someone will react. Both the orange and green represent strong feelings in Ireland and in Northern Ireland. Even if you aren't confronted, why put someone off, even if you don't mean to. Remain neutral.

I wore a bright green raincoat in September with no problem. No one hissed or spit on me.

I continue to advise anyone visiting Belfast during the period leading up to the Orange Order observances of July 12 to perform your own due diligence regarding the local marching season as well as the potential sectarian tensions that may accompany them. Reports of incidents such as this one https://www.theguardian.com/uk-news/2018/jul/12/northern-ireland-orange-order-parades-12-july-amid-violence-belfast-derry should be enough to give anyone pause, as well as providing evidence that our personal experience of a few years ago wasn't exactly an isolated occurrence.
Do your own research, then make up your own mind.

Handy that we now have a new local poster to answer queries.

Thanks james!

Thanks to everyone for their contributions. The OP's question seems to be addressed and I'm locking the thread to avoid certain issues that seem to keep cropping up in this thread.