Did Buddhism oppose Vedic religion? At the time of Tathagat Buddha, Hindu religion in its current form did not exist. However, there were Vedic teachings. These teachings were based on blind belief in the authority of the Vedas. There were many different schools of philosophy opposing Vedic teaching, e.g. Akriyavada, Niyativada (determinism), Ucchedavada etc. 

As far as I know, the Buddha opposed Vedic religion. He opened a strong camp against it and freed people from the exploitative teachings of Veda. He expounded equality as opposed to the Vedic teachings which discriminated between different classes. 

Is it true that Buddhism (since time of Buddha) opposed Vedic (and later Brahminical) religion?
In his Great Minds of the Eastern tradition lecture series Grant Hardy identifies 6 orthodox schools of Indian philosophy (Samkhya, Yoga, Nyaya, Vaisheshik, Mimāṃsā, Vedanta). He also identified 3 heterodox schools 


Cārvāka (materialist) 
Jainism  
Buddhism


The heterodox schools are those who reject the authority of the Vedas. So based on this then Buddhism was opposed to the Vedic religion.Interestingly the Buddha came to be seen as an avatar of the god Vishnu in some forms Hinduism. I guess that it's better to have the Buddha inside the tent chanting out then outside the tent chanting in (or words to that effect).