Copodope Gopolopfop

Retina, 9 bytes

(?!\G)op

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Instead of checking that the preceding character is a consonant, we just make sure that the current op is not adjacent to either the beginning of the string or the previous match. The only case where we could match an incorrect op is if the original string contained an op (resulting in opop). But in that case we'll just remove the first op instead of the second and the result will be the same.

Python, 42 bytes

lambda s:re.sub('(.)op',r'\1',s)
import re

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If I'm not mistaken, you can just substitute all ?op with ? without caring about vowels. If the original string contains op, then it's oppified to opop, and the replacement returns it to op and no further. This is because the pattern matches for ?op cannot overlap, so only one op is removed.

A non-regex solution is 5 bytes longer.

Python, 47 bytes

f=lambda s:s and s[0]+f(s[1+2*(s[1:3]=='op'):])

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V, 12, 5 bytes

Í.“op

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00000000: cd2e 936f 70                             ...op

Saved 7 bytes thanks to @Xnor's realization that since the input must always be opped, we don't have to check for vowels.