Believing in superstitions on Tuesdays

If a Muslim brother’s family believes in Tuesday being an unlucky or a bad day due to possibly bad things happening in the past on Tuesdays or a holy peer telling the brother’a family that Tuesday is an unlucky/bad day for their family.

Therefore this Muslim brother’s family dont have haircuts, bathe, wash clothes etc on Tuesdays.
But this Muslim brother does not believe in the above explained family superstitious belief, however he still is scared to have haircuts, bathe,wash clothes etc on Tuesdays and therefore doesn’t do such things on a Tuesday. Does this Muslim brother lose his imaan by being scared and still not doing things as explained above on Tuesdays just in case something bad happens, even though he doesn’t believe in this superstitious belief?

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