Replacing Cheddar Cheese in Taquito's

Most supermarket will have mexican cheeses. None of which are Cheddar.
Here's a guide: http://www.mexconnect.com/articles/2155-a-guide-to-mexican-cheese-queso-mexicano

what you'd want is Mexican "Melting cheese" . Queso asadero (jack is a good sub) or Queso oaxaca which is also a great sub for mozzarella.

How about Jack cheese?

I agree with Phillip for the most part (I just don't think there's anything particularly inauthentic about Monterey Jack or a whole-milk mozzarella. Given your aversion to cheddar, I'd suggest either (assuming the application calls for a melting cheese).

Cream Cheese would definitely not be my first choice for replacing cheddar. Something gratable will give you a more similar texture profile. Monterrey Jack or even a Mozzarella would be close. For a more Mexican cheese you could try cojito or one of the similar white, milld, crumbly cheeses (almost similar to Feta now I think about it.)

All that said, Taquitos or their close relative Flautas without cheese at all are relatively common in the Tex Mex/MexMex I grew up with around Houston. I think you could forego the cheese altogether, especially if you plan on serving them alongside sour cream, salsa, or guac for dipping.

Is there a specific recipe you are following? I'm sure cream cheese (or really, any other cheese you feel like) would be fine. I would just try to make sure whatever cheese I used acted as a textural/taste contrast to the other ingredients.