Yes, and we will need to go back to the days even before the Malayan Federation was formed.

The migrant population back then (Chinese, Indians etc) were still very young, in fact during the days of Independence many ware just starting their family. Many still hold a sense of belonging with their native land, and as such, not many of us participate actively in the early nationalist movement. In fact, in the case of the Chinese associations, they are more interested in the developments in China rather than Malaya, and we Straights Chinese are famous for our reverent support for Sun Yat Sen & our contribution had ensured the success of the Chinese Revolution.

On the other hand, the Malays inteligensia gradually organised themselves, forming early literary movements that calls for Malays to protect their birthright, ie land rights, and religion, also to encourage literacy. Their ultimate achievement was the establishment of UMNO, an organization large enough to speak for the whole Malay population in Malaya back then, and was the most powerful political party in Malaysia until the last general election.

Some say that the old colonial policies that had resulted in our racial based political system, but I would attribute this more to the slow rise of national identity in the non Malay population.

That said, cross racial parties did exist back then, ironically one was founded by the founder of UMNO himself, but support was lackluster.

I would suggest reading on the expulsion of Singapore too if you want to know how the political climate was back them. It wasn't pretty.