Rav Shlomo Aviner, a major posek of the Chardali (charedi-leaning dati leumi) community, recently answered this very question, in one of his mini-teshuvos. He’s not known for leniencies himself, as far as I know. Here’s the quote from his website:
“Q: In theory, is it permissible for me to always search out a Rabbi who is lenient?
A: Yes. One who wants to follow Beit Shammai may do so, one who wants to follow Beit Hillel may do so. Eruvin 6b. But not leniencies which contradict one another.”