SNP sports spokeswoman Hannah Bardell said sexist and homophobic attitudes still prevail in many sports.
She spoke of her disappointment at seeing tweets mocking the Scottish women's national football team's appearance in the World Cup, with one saying it was only worth watching for "the possibility of tits and fanny".
She branded the tweets "sexist" and said she hopes Twitter will "take swift action" against comments like this.
Sport secretary Jeremy Wright said discrimination and abuse are often levelled at players and athletes themselves, and that more should be done to protect them.
Mr Wright said he has been "appalled" by recent incidents of discrimination in English stadia and said players should not be punished if they decide to leave the pitch due to abuse from spectators.
He said: "My view is that if players decide they want to stay and respond with their skills on the pitch, then we should support them in that and have huge respect for their resilience and professionalism.
"But I also strongly believe that players at any level should not suffer any disadvantage, penalty, or sanction if they choose to make a stand and walk off the pitch. We should respect those decisions too."
Speaking during the debate, shadow sport minister Rosena Allin-Khan said better education is the key, and that some groups are exploiting sports, particularly football, to further extreme ideologies.
Dr Allin-Khan said: "With the far-right on our doorstep, let's be aware of their attempts to infiltrate football and other sports.
"Let's ensure we are brave in speaking up against them. When combating the far-right, education is an extremely effective tool."
She added: "Innocent fans can get caught up in unsavoury actions."