What tenets must a person accept to be a Buddhist?
You just need to take refuge in the Triple Gem sincerely.


Buddham saranam gacchami - I go to the Buddha for refuge. 
Dhammam saranam gacchami - I go to the Dhamma for refuge.
Sangham saranam gacchami.- I go to the Sangha for refuge.


Refuge here means spiritual refuge. It doesn't mean you reject medicine for physical ailments like in some Christian sects.

Taking refuge will be broken for ordinary people when they die, but this breaking is blameless and does not bring bad results. On the other hand, breaking the taking of the Triple Refuge during one's life is very serious. This is broken whenever a person goes for refuge to a teacher outside the Buddha's Dispensation or when a person is disrespectful to the Triple Gem. Those who are Noble Ones will never break with their refuge. But ordinary people, through ignorance, doubt, and wrong knowledge about the special qualities of the Buddha, the Dhamma, and the Sangha, are susceptible to breaking their refuge. 

Read more at How to Take the Triple Refuge.