Firstly, as ChrisW mentioned, a person might do this to please others. For example, in this case, a Buddhist politician may partake in a ceremony in another religion's place of worship to make other people happy. For example, here is a news article on Indian PM Narendra Modi visiting a Hindu temple, a Buddhist temple and a mosque in Singapore. I'm not sure if he participated in any religious ceremonies.
Secondly, a person might do this to fit in. For example, a member of Buddhism.SE who is a practising lay Buddhist from a Muslim background, wrote an answer here (which I think I won't provide the link for), stating that he did not openly declare himself to be a Buddhist and instead lives an outward life appearing to be a Muslim, whenever he meets his relatives. I'm only paraphrasing the answer, according to my understanding of it.
Thirdly, lay Buddhists and even some monks may participate in what appears to be superstitious rituals, even if the Buddha discouraged this. Just because some people identify themselves as Buddhist, doesn't mean that they are aware of the Dhamma (teachings).
For example, from this article:
This leads to the highlight of the day - chanting and blessings by
monks and ending the short session (which lasts no more than 5
minutes) with a shower of "holy water".
The monks softly chants a Thai variety of the Ti-Ratana Vandana
(homage to the Triple Gem), five precepts and punnanumodana (sharing
of merits). For most however, these chants are exotic and spiritual,
and are perceived to have "supra mundane" powers. It is no wonder
then that many devotees place their personal belongings - amulets,
religious icons and even car keys - onto a tray held by the monk who
performs the chanting.
Their belief - mistaken or otherwise - is that these chants contain "spiritual powers" which are then transcended into their items, which
when worn or used, protects them from harm or danger. The ceremony
ends with the tying of yellow coloured strings on the wrist, a
symbolic notion of the presence of the Sangha in the laity. Of course,
if one wishes, they can also make a donation to the monk concerned for
his service by putting money into a metal box.
Lastly, to answer your question:
OP: Is Buddhism free from all superstitious blind beliefs or it is just an simple offshoot of Hinduism / Brahmanism ?
If by Buddhism, you are referring to what the Buddha taught, then the following passage from DN 2 would be self-explanatory. You might also be interested in "Is Buddhism just Hinduism stripped for export?".
"Whereas some contemplatives & brahmans, living off food given in
faith, maintain themselves by wrong livelihood, by such "animal" arts
as: reading marks on the limbs [e.g., palmistry]; reading omens and
signs; interpreting celestial events [falling stars, comets];
interpreting dreams; reading features of the body [e.g., phrenology];
reading marks on cloth gnawed by mice; offering fire oblations,
oblations from a ladle, oblations of husks, rice powder, rice grains,
ghee, and oil; offering oblations from the mouth; offering
blood-sacrifices; making predictions based on the fingertips;
geomancy; making predictions for state officials; laying demons in a
cemetery; placing spells on spirits; earth-skills [divining water and
gems?]; snake-skills, poison-skills, scorpion-skills, rat-skills,
bird-skills, crow-skills; predicting life spans; giving protective
charms; casting horoscopes — he abstains from wrong livelihood, from
"animal" arts such as these.
"Whereas some contemplatives & brahmans, living off food given in
faith, maintain themselves by wrong livelihood, by such "animal" arts
as: determining lucky and unlucky gems, staffs, garments, swords,
arrows, bows, and other weapons; women, men, boys, girls, male slaves,
female slaves; elephants, horses, buffaloes, bulls, cows, goats, rams,
fowl, quails, lizards, rabbits, tortoises, and other animals — he
abstains from wrong livelihood, from "animal" arts such as these.
"Whereas some contemplatives & brahmans, living off food given in
faith, maintain themselves by wrong livelihood, by such "animal" arts
as [forecasting]: the rulers will march forth; the rulers will not
march forth; our rulers will attack, and their rulers will retreat;
their rulers will attack, and our rulers will retreat; there will be
triumph for our rulers and defeat for their rulers; there will be
triumph for their rulers and defeat for our rulers; thus there will be
triumph this one, defeat for that one — he abstains from wrong
livelihood, from "animal" arts such as these.
"Whereas some contemplatives & brahmans, living off food given in
faith, maintain themselves by wrong livelihood, by such "animal" arts
as [forecasting]: there will be a lunar eclipse; there will be a solar
eclipse; there will be an occultation of [a conjunction of the moon or
a planet with] an asterism; the sun and moon will be favorable; the
sun and moon will be unfavorable; the asterisms will be favorable; the
asterisms will be unfavorable; there will be a meteor shower; there
will be a flickering light on the horizon [an aurora?]; there will be
an earthquake; there will be thunder coming from dry clouds; there
will be a rising, a setting, a darkening, a brightening of the sun,
moon, and asterisms; such will be the result of the lunar eclipse ...
the rising, setting, darkening, brightening of the sun, moon, and
asterisms — he abstains from wrong livelihood, from "animal" arts such
as these.
"Whereas some contemplatives & brahmans, living off food given in
faith, maintain themselves by wrong livelihood, by such "animal" arts
as [forecasting]: there will be abundant rain; there will be a
drought; there will be plenty; there will be famine; there will be
rest and security; there will be danger; there will be disease; there
will be freedom from disease; or they earn their living by accounting,
counting, calculation, composing poetry, or teaching hedonistic arts
and doctrines [lokāyata] — he abstains from wrong livelihood, from
"animal" arts such as these.
"Whereas some contemplatives & brahmans, living off food given in
faith, maintain themselves by wrong livelihood, by such "animal" arts
as: calculating auspicious dates for marriages — both those in which
the bride is brought home and those in which she is sent out;
calculating auspicious dates for betrothals and divorces; for
collecting debts or making investments and loans; reciting charms to
make people attractive or unattractive; curing women who have
undergone miscarriages or abortions; reciting spells to bind a man's
tongue, to paralyze his jaws, to make him lose control over his hands,
or to bring on deafness; getting oracular answers to questions
addressed to a spirit in a mirror, in a young girl, or to a spirit
medium; worshipping the sun, worshipping the Great Brahmā, bringing
forth flames from the mouth, invoking the goddess of luck — he
abstains from wrong livelihood, from "animal" arts such as these.
"Whereas some contemplatives & brahmans, living off food given in
faith, maintain themselves by wrong livelihood, by such "animal" arts
as: promising gifts to deities in return for favors; fulfilling such
promises; demonology; reciting spells in earth houses [see earth
skills, above]; inducing virility and impotence; preparing sites for
construction; consecrating sites for construction; giving ceremonial
mouthwashes and ceremonial baths; offering sacrificial fires;
administering emetics, purges, purges from above, purges from below,
head-purges; ear-oil, eye-drops, treatments through the nose,
ointments, and counter-ointments; practicing eye-surgery [or:
extractive surgery], general surgery, pediatrics; administering
root-medicines and binding medicinal herbs — he abstains from wrong
livelihood, from "animal" arts such as these. This, too, is part of
his virtue."
"A monk thus consummate in virtue sees no danger anywhere from his
restraint through virtue. Just as a head-anointed noble warrior king
who has defeated his enemies sees no danger anywhere from his enemies,
in the same way the monk thus consummate in virtue sees no danger
anywhere from his restraint through virtue. Endowed with this noble
aggregate of virtue, he is inwardly sensitive to the pleasure of being
blameless. This is how a monk is consummate in virtue.