Learn Finnish: Silmukka on nopea koodata.

Because silmukka is acting as the grammatical subject of the sentence. In Finnish, when an evaluative sentence has a clear nominative subject, the adjective agrees with it and also takes the nominative case. If there were no subject (e.g., "It is fast to code"), you would use the partitive: On nopeaa koodata.

Since the loop is the thing being coded, why isn't silmukka treated as an object?

This is a special feature of this exact sentence structure (olla + adjective + 1st infinitive). The logical object of the action (silmukka) moves to the front of the sentence to become the grammatical subject. Because it is the subject, it takes the basic nominative case.

Could I say On nopeaa koodata silmukka instead?

Yes, that is also perfectly correct and translates to "It is fast to code a loop." Notice that when you use this word order, the sentence starts with on and lacks a grammatical subject, so the adjective shifts to the partitive case (nopeaa).

What verb type is koodata and why doesn't it conjugate here?

Koodata (to code) is a Type 4 verb, which ends in -ta or -tä. It doesn't conjugate because this evaluative structure requires the basic dictionary form of the verb (the 1st infinitive). It connects directly to the adjective, exactly mirroring the English pattern "fast to code".