"Follow religiously" in a non religious context

Solution 1:

You should check zealously.

Support will agree with their candidate's views zealously despite being obviously flawed, as he is their candidate.
Interns suck up to the decision maker zealously to gain favour and get access to their network.

Someone who is zealous is just driven by their zeal towards their ultimate aim (in the context) like making the candidate win or gain favour of the target person, so they may end up blindly supporting them.

M-W:

zealous adjective

: marked by fervent partisanship for a person, a cause, or an ideal : filled with or characterized by zeal : zealous missionaries

• zealously adverb

zeal noun

: eagerness and ardent interest in pursuit of something : fervor : her zeal to succeed strained her relationships

partisan noun

1 : a firm adherent to a party, faction, cause, or person; especially : one exhibiting blind, prejudiced, and unreasoning allegiance

• partisan adjective
• partisanly adverb
• partisanship noun