But these are only your ideas, Mint, regarding what the hypothetical priest would do in such a situation. Please note that in the past Dzogchen was considered to be a heresy, and because of that villified, by quite a few Vajrayana masters - and some of the students of these masters did practice Dzogchen in secret; they surely weren't hypocrites, were they?
These days Namkhai Norbu has got a lot of Gelugpa students who may also happen to wish to keep their Dzogchen practice secret - and he does have, or so I am told, both lay Christians and Christian monks as students, who may be facing a similar dilemma. Yet they do stay Christian, and don't get disrobed - are we arrogant enough to acuse them of hypocrisy without knowing their reasons for what they do or fail to do?
If they cling to illusions such as Christ and God, they don't practice Dzogchen.