Is celibacy important to spiritual evolvement?
Is abstaining from all forms of sexual play vital for spiritual progress?

Spiritual progress is hampered by disharmonious things.
That is things that are not harmonious with your true nature, love.
When whatever you do (and have) is loving, it helps your spiritual
evolvement.
When your sexual relations and playing are loving, you are not weakened
by them.
What does it mean "loving"?
The following can be substituted for "loving":
- highly energized
- truly healthy
- harmonious with love
- congruent with Divine Loves (Gods)
- harmonious with joy, bliss, positive fun, justice, peace, understanding, truth

A healthy individual may have loving sex and live with a healthy partner
while remaining spiritually strong and evolving.
So celibacy and abstaining from sexual playing are not important for
spiritual progress by themselves.
It is true that getting involved relationship-wise and/or sexually-wise
with someone who is not healthy and/or for unloving reasons can
negatively affect the individual and thwart his/her spiritual advancement,
and even bring about his/her spiritual fall.   (The unloving reasons could
be: lust; want to control; wish to feel "complete"; addiction to sex; living
through sex; living through others.)
There may be instances when it is better to embrace celibacy and to
abstain from sexual playing, such as: poor health of the individual; lack
of energy; toxicity; energy system fragmentation.   However, that abstinence
comes out of understanding, not out of suppression.
To decree that a certain class of people should be celibate lacks intelligence,
and the individuals who accept that decree automatically do more harm
to themselves than good, because that equals suppression.
As you can read on this page, celibacy can be healthily attained only
through sexual maturity or good health.   Sexual suppression can lead
to sexual, mental, emotional, and spiritual problems.

Some people might think that sex and sexual playing are lower energy
or lower chakra activities, distracting from spiritual endeavors.
While the body and its functions may not be as highly energized as
some spiritual activities, a healthy individual has enough energy to channel
it in any congruent way.   There is nothing wrong with using the body for
healthy fun; of course, it is important to be aware that the body is just
a temporary thing and not the true "you" (= non-attachment).
It is true that eventually the spiritual aspirant drops sex and
sexual playing (embraces celibacy) naturally via understanding,
when he/she evolves high enough.   It is important to repeat
that this happens naturally; nothing is forced, nothing is suppressed.
Suppressing one's sexually energy by forcing celibacy (such as done
by the Catholic Church to its clergy) is a sure recipe for psychological
issues.   The sexual energy flow is like a powerful river;
it cannot be stopped just because one decides to stop it ouf of
a belief or a doctrine; it can be elevated to a spiritual energy
flow via understanding that comes from the Divine when the spiritual
student's energy reaches high-enough level.

Above you have read the terms "congruent with" and "harmonious with".
They both mean the same thing.   This "congruence with" is vital in everything
you do, intend to do, and possess.   Incongruent (disharmonious) actions,
connections, and possessions weaken you.
The best way to find out if you are congruent with whatever you want to do
or have is to visit a doctor that performs Neuro-Emotional Technique (NET),
and get tested.   NET can quickly reveal an incongruence (disharmony) and
can help resolve it.