There is a distinction between Hindu culture and Hindu spirituality.
In Hindu culture, one is born into a Hindu family, and into a caste, either Sudra (working class), Vaishyas (merchant class) Kshethriya, (warriors and rulers) or Brahmin (priestly class). A Hindu initiated via the sixteen samkaras (sacraments) and progresses through the various stages (ashramas) of life: brahmacharya (student life), grihahasta (marriage), varnaprasta (retirement) and sanyasa (old age and detachment, letting go). A Hindu pursues the four goals of life: artha (wealth) dharma (right conduct), kama (desires) and moksha (release from the cycle of rebirth). All these goals have to be pursued in balance or life goes out of balance.
Hindu spirituality is about knowing God as hrudaya vasi, the indweller of the heart. Hindu spirituality is a balance of selfless service, spiritual effort, yearning for the divine and common sense. In these days, due the spread of Hinduism to many countries, you may find white people in India wearing the bindu dot or a smear of vibhuti (sacred ash) between the eyes, marking the third eye. They may wear western dress or traditional Indian dress, or even dress themselves like a typical spiritual aspirant (bhakta) in the traditional Hindu manner with a sari or a lungi.
Whatever you call the Supreme Being, however you picture him or her, whatever name you give to him or her, there is an inner core of genuine mystical experience that links all religions together: the search for the experience of the divine. Hinduism has many techniques to achieve that experience, and as it is the oldest religion of humanity, these techniques have been tried and tested and found to be true over millennia by rishis, sadhaks, bhaktas, saints (sants) and ordinary people.
Nothing prevents you from following your own program of spiritual discipline, or spiritual effort (called Sadhana in Hinduism). Be cheerful, be of good nature, be of common sense and spiritual sense. All prayers and sacrifices reach the House of the Divine. All genuine spiritual effort from the heart marks progess. There are many ways up the mountain to the top.
We finish with a poem from Ralph Waldo Emerson, titled Brahma
If the red slayer think he slays,
Or if the slain think he is slain,
They know not well the subtle ways
I keep, and pass, and turn again.
Far or forgot to me is near;
Shadow and sunlight are the same;
The vanished gods to me appear;
And one to me are shame and fame.
They reckon ill who leave me out;
When me they fly, I am the wings;
I am the doubter and the doubt,
And I the hymn the Brahmin sings.
The strong gods pine for my abode,
And pine in vain the sacred Seven;
But thou, meek lover of the good!
Find me, and turn thy back on heaven.