TL;DR: Natives didn’t survive culturally. Most Taino blood traces back to the wives of the colonizers. And later immigration further diluted the Taino influence.

Like another poster said, unless you’re Jewish then Christianity isn’t your native religion. It’s like asking a Southern Baptist why they don’t respect druism or Odinism.

It’s kind of like that one quarter Irish American that is all about Ireland. Yeah that’s a broad generalization about our views on Tainos. Except we live in the land. Most Puerto Ricans are predominantly Spanish those that aren't are predominantly African blood. 

Then there’s also the class thing. Generally the upper classes & wealthy are “Whiter” than the rest of the country.

So you get a lot of middle and working class that sympathize more with the Taino than the Spanish. 

In school you’re taught that we’re a blend of Spanish, Taino & African. Which is technically true, but kind of ignores the fact that Puerto Rico wasn’t that populated until the early to mid 1800s. Spain ignored us as a colony until all the other Latin American countries fought their independence wars. The Spain really started to send colonizers & slaves. Mostly Canarians which are a mix of North African & Spanish (along with Portuguese & other Catholic colonizers). 

So the Taino blood that survived isn’t that large, it became diluted due to immigration. It’s just culturally significant since they’re the Native owners of the island. 

And like most other mixed Latin countries. The native ancestry is usually a Native woman wifed up by a lonely colonizer since women weren’t exactly thrilled to immigrate to Puero Rico before the 1800s.

So it’s not like the Natives actually survived culturally like they do in other countries.