Women are exempt from positive mitzvot that are dependent on a particular time, מצות עשה שהזמן גרמא. That includes mitzvot such as shofar, lulav, tzitzit and tefillin.
Exempt means exempt.
It does not mean prohibited.
So a woman does not have to hear shofar on Rosh Hashanah. If she wants to hear it, wonderful. If she has young children at home, is exhausted, cannot get to shul, or simply does not take on that voluntary mitzvah, she has done nothing wrong.
I think it is unfair when communities create tremendous pressure on women to get to shul for shofar as though they are obligated. Halachah specifically exempted them.
The same basic principle works in the other direction.
If a woman wants to perform a time-bound mitzvah from which she is exempt, generally she may do so.
An Ashkenazi woman following the Rema may make the berachah on a mitzvat aseh shehazman grama that she voluntarily performs. According to the Sephardic practice following the Shulchan Aruch, she performs the mitzvah without saying the berachah of וצונו.
There are later restrictions discussed regarding particular mitzvot.
For example, with tefillin there is a requirement of גוף נקי. Fine. That requirement applies to men too.
If a person cannot properly maintain a guf naki, that person should not be wearing tefillin.
But I do not see why an educated woman today who understands the halachot and knows how to maintain a guf naki should automatically be treated differently from an educated man who understands exactly the same thing.
Likewise, sometimes the Poskim speak about יוהרא, an act appearing ostentatious or pretentious.
But yuhara is inherently dependent on circumstances.
Something that appeared strange and ostentatious in one society at one period in history does not automatically remain yuhara forever. Social circumstances change.
That is an important principle whenever we learn restrictions that were based upon a particular reality. First understand why the restriction existed. Then ask whether that reality still exists.
Women today are educated. They study Torah, medicine, law, science, business and every other sophisticated subject. There is no intellectual reason that a woman who wants to learn the halachot of tefillin cannot understand them just as well as a man.
So in my opinion, there is no general reason today that a woman who understands the requirements and wants to put on tefillin cannot do so.
But there is also absolutely no reason to pressure her to do it.
That is the part that I think gets lost.
A woman does not need to hear shofar.
She does not need to shake a lulav.
She does not need to wear a tallit.
She does not need to put on tefillin.
If she wants to perform one of these mitzvot voluntarily, that is a different question, and the particular halachot of that mitzvah have to be observed.
But do not turn voluntary mitzvot into obligations, and do not turn exemptions into prohibitions.
Both mistakes distort the Halachah.
The starting point is simple:
פטור does not mean אסור.
And voluntary does not mean required.