In one incident at a NSW TAFE function, a group of white men in their 20s and 30s in the audience were seen mimicking and ridiculing a Welcome to Country and traditional dance performance.
He said an Indigenous woman in front of them in the audience told him what happened after she turned around to ask the men to show some respect. But no one else had backed her up. She was reduced to tears and felt so uncomfortable she had to leave the event.
"We can't put a stop to racism by only having people of colour speak out about it. Racism is everybody's business", says Mr Williams.
In the other incident, an Indigenous worker at a childcare centre, where some staff and patrons were Aboriginal, asked the centre if they could run an event during NAIDOC week.
"The staff member was told, 'if you would like to celebrate it, you organise it', with little to no support from the non Indigenous executive and staff. She was laughed at and turned away by her boss because she wanted her work place to celebrate NAIDOC week".
He said both incidents showed there was much further to go on the road to equality.
"With many communities around the country celebrating NAIDOC week we hear so many positives, that one would be inclined to think that the country we are all so proud to call home; is moving forward together harmoniously".
But the childcare centre could have supported their staff by celebrating NAIDOC week and, by doing so, played a role in the national reconciliation process.
Mr Williams said it was a chance to highlight "how special our culture really is".
"These two examples are just two [of] many we see every day in our communities. We must continue our fight together, both First Nations and non-Indigenous [people], to build a brighter future for our generations to come."