"[...] a key aim for meditation is to be with whatever thoughts and feelings are present, without trying to change anything."
Regarding the "without trying to change anything" part, this advice is a popular (but often confusing) way of teaching equanimity (pali: upekkha), an important skill in the Buddhist curriculum. In a sense, the advice's purpose seems to aim both at preventing mindless habitual reactions to a certain event and preventing reactions based on aversion (pali: dosa) or craving (pali: taṇhā), two of the five hindrances that prevent us from progressing.
In Compassion and Emptiness in Early Buddhist Meditation, Ven. Analayo explains equanimity as follows:
"Equanimity or equipoise, upek(k)ha, from the etymological perspective suggests a mental attitude of 'looking upon', not an indifferent 'looking away'. The term thus conveys an awareness of whatever is happening combined with mental balance and the absence of favoring or opposing."
[...] "equanimity is [...] a mental equipoise that rounds off a systematic opening of the heart which has been brought about through cultivation of the other three divine abodes".
Here's, for example, how the Buddha teaches the development of equanimity in the suttas:
"Now how, Ananda, in the discipline of a noble one is there the unexcelled development of the faculties?
"[...] when touching a tactile sensation with the body, there arises in a monk what is agreeable, what is disagreeable, what is agreeable & disagreeable. He discerns that 'This agreeable thing has arisen in me, this disagreeable thing... this agreeable & disagreeable thing has arisen in me. And that is compounded, gross, dependently co-arisen. But this is peaceful, this is exquisite, i.e., equanimity.' With that, the arisen agreeable thing... disagreeable thing... agreeable & disagreeable thing ceases, and equanimity takes its stance. Just as a strong man might easily extend his flexed arm or flex his extended arm, that is how quickly, how rapidly, how easily, no matter what it refers to, the arisen agreeable thing... disagreeable thing... agreeable & disagreeable thing ceases, and equanimity takes its stance. In the discipline of a noble one, this is called the unexcelled development of the faculties with regard to tactile sensations cognizable by the body.
-- Indriya-bhavana Sutta, MN 152 (Thanissaro Trans.)
As illustration, here's a sutta narrating the attitude of the Buddha when in physical pain:
I have heard that on one occasion the Blessed One was staying near Rajagaha at the Maddakucchi Deer Reserve. Now at that time his foot had been pierced by a stone sliver. Excruciating were the bodily feelings that developed within him — painful, fierce, sharp, wracking, repellent, disagreeable — but he endured them mindful, alert, & unperturbed. Having had his outer robe folded in four and laid out, he lay down on his right side in the lion's posture, with one foot placed on top of the other, mindful & alert.
-- SN 1.38
It's important to note that equanimity is not some kind of passivity as if one should remain idle when facing a threat to one's health. One should still take care of one self and others equanimously － instead of trying to take care of oneself and others moved by fear, despair, anger or craving.
Another related sutta is the The Arrow which illustrates the differences between pain and suffering.
"However, in my practice I have found that if I consciously try to relax during a session (muscular tension is an issue with me) it can be a much more fulfilling, refreshing experience."
During meditation, specially, the samatha aspect of the practice, that's good. Here's the Buddha describing his own experience:
[...] But with excessive thinking and pondering I might tire my body, and when the body is tired, the mind becomes strained, and when the mind is strained, it is far from concentration. So I steadied my mind internally, quieted it, brought it to singleness, and concentrated it. Why is that? So my mind should not be strained.
-- Dvedhāvitakka Sutta [Bodhi trans.], MN 19
So, as you can see, "consciously trying" is necessary in the Buddhist training. Knowing what to try to do and what to prevent doing, however, requires understanding what are wholesome actions and attitudes (those leading to enlightenment) and unwholesome actions (those that lead to more suffering) as well as knowing the skills and goals to be developed during a certain practice.
On the importance of equanimity, it is an important factor in many doctrinal aspects, among them, the 7 enlightenment factors. They are:
- Mindfulness (sati)
- Investigation (dhamma vicaya)
- Energy (viriya)
- Joy or rapture (pīti)
- Relaxation or tranquility (passaddhi)
- Concentration (samādhi)
- Equanimity (upekkha)
On the five hindrances:
“Bhikkhus, there are these five hindrances. What five? The hindrance of sensual desire, the hindrance of ill will [aversion], the hindrance of sloth and torpor, the hindrance of restlessness and remorse, the hindrance of doubt. These are the five hindrances. This Noble Eightfold Path is to be developed for direct knowledge of these five hindrances, for the full understanding of them, for their utter destruction, for their abandoning.”