This argument is behind the notion of 'lusotropicalism', as I understand it.
At the superficial level, there appears to be some proof; Brazil has an enormous mixed African/European population, whereas countries with comparative slave histories like the USA have a much smaller one.
In practice, did the Portugese place less emphasis on race than other powers?
I'll start by saying that I'm not knowledgable enough about the situation in Brazil to be making any claims about it. My answer is mostly relevant to Portuguese Imperialism in Africa and the Indian Ocean.
Racism is not a metric that's easily measured, but a general comparisson through examples is definitely possible. I'll do this mainly through arguments provided in C.R. Boxer's Race Relations in the Portuguese Colonial Empire, 1415-1825. Note that this work dates from 1963, when Portugal still held several African colonies and there was a strong anti-imperialist sentiment amongst Anglo-American academics. Boxer tried to paint himself as a centrist on the issue by being as neutral as possible in his observation of the facts. Nonetheless, his work was controversial amongst the Portuguese imperialist academics and Salazar regime, who were trying very hard to get Luso-tropicalism recognized by the international academic world.
Generally, Boxer argued that history could not be used as an argument for Salazar's ideology of racial cohabitation and integration. The clearest example of racial segregation in India is the formation of a native clergy amongst the converted Muslims and Hindus. Jesuits in the second half of the 16th century report that the Portuguese refused to go to confession with a native priest as they felt strongly that only a European clergyman could perform the ritual.
An example I like to give myself is that of Afonso de Albuquerque, the Second Viceroy of India. His policy was a rather tolerant one despite his hatred for Islam being clear in his letters. His tolerance was mostly pragmatic, however, as he needed the (military) cooperation of the natives. His policy of encouraging marriages between Portuguese soldiers and converted Indians can also be explained through the pragmatic need for a stable colonial population rather than a desire to integrate with the native population. Despite the need for these policies, they were still highly controversial and Afonso needed to constantly defend himself to the king. This is why we have such such a large amount of preserved correspondence between him and the king in the first place. Going back to the marriage policy, Afonso defended it by claiming Muslims and high-caste Hindus were "as good as white", so there was definitely a racially discriminating argument being made against his policies.
As a conclusion, C.R. Boxer does bring a comparative element into his work that shows the racial discimination in the Portuguese Empire was not as severe as in other colonial empires. This relativises it somewhat, but as shown by the examples, the Portuguese Empire was nowhere near as racially inclusive and integrated as 20th century proponents of luso-tropicalism liked to claim.
BOXER, C.R., Race Relations in the Portuguese Colonial Empire, 1415-1825, London, 1963.
DE ALBUQUERQUE, A., The Commentaries of the Great Afonso Dalboquerque, Second Viceroy of India: Translated from the Portuguese Edition of 1774, W. DE GRAY BIRCH (translation), I-IV, London, 1875.
DE MENDONÇA, D., Conversions and Citizenry: Goa under Portugal, 1510-1610, New Delhi, 2002.
SCAMMELL, G.V., 'Indigenous Assistance in the Establishment of Portuguese power in Asia in the Sixteenth Century', Modern Asian Studies, 14 (1980), 1-11.
^Edit: ^Typos.