Watson-Crick palindromes
05AB1E, 10 7 bytes

Code:

Â'š×Â‡Q


Explanation:

To check if a string is a palindrome, we just need to check the input with the input, with at swapped and cg swapped and then reverse it. So that is what we are going to do. We push the input and the input reversed using Â (bifurcate). Now comes a tricky part. 'š× is the compressed version for creating. If we reverse it, you can see why it's in the code:

CreATinG
|  ||  |
GniTAerC


This will be used to transliterate the reversed input. Transliteration is done with ‡. After that, we just check if the input and the transliterated input are eQual and print that value. So this is how the stack looks like for input actg :

Â          # ["actg", "gtca"]
 'š×       # ["actg", "gtca", "creating"]
    Â      # ["actg", "gtca", "creating", "gnitaerc"]
     ‡     # ["actg", "cagt"]
      Q    # [0]


Which can also be seen with the debug flag (Try it here).

Uses CP-1252 encoding. Try it online!.