On Kol BeRama radio Rav Ahron Butbol was asked a quesion about this type of behavior.

A listener asked if it is ok to register for Likud membership so as to support a specific candidate who is religious in his candidacy for a slot on the Likud list. the questioner mentioned that until now he has refused to do so so as to avoid strengthening a secular political party, but ont he other hand perhaps continuing to refuse actually leaves the field open to anti-religious elements and leaves it open to the opposite of what he wants - he wants the Likud to get closer to more religious positions, but leaving it because it isnt a religious party (at least officially) leaves it to be more influenced by anti-religious...

Rav Butbol said that on election day voting for a secular party is a problem because that strengthens a secular party, but the request here is not to actually vote for the Likud but to register so as to vote in the primaries and support a religious candidate. It is problematic to do so because the Haredi public is committed and obligated to vote for the Haredi and religious parties. However, registering for internal elections is a tool to influence the identities of their representatives and is not necessarily considered supporting the platform of the party.

Rav Butbol points out there were three Likud MKs who torpedoed the progress of the Draft law. The PM could not do anything about it. They were elected to Likud slots in the Likud primaries. If the public with a connection to tradition would be more involved in the internal elections in the Likud, candidates who keep tradition and religious values can be elected and the Likud could be turned into a party that protects the Torah world more. 

Before continuing I would note that MKs Edelstein and Ilouz are both religious and still chose to oppose the law that was being presented.

To conclude, Rav Butbol paskened that if the candidate is recognized as a good decent person with a strong and true connection to religion and tradition, there is a strong reason to register to help him be elected. This would not be considered "assisting a chilul hashem" but the exact opposite - strengthening the Torah positions in other political strongholds.