Two obvious examples being the Dalai Lama and Thich Nhat Hanh who both have advocated for political freedoms of all people but especially in their homelands of Tibet and Vietnam.
In fact, Zen master Hanh has developed a form of socially active Buddhism called, "Engaged Buddhism" which teaches Dharma practitioners on how to apply Dharma lessons to real world challenges such as social, political and economic realities. His aim, however, isn't necessarily to favor one political side over another. In fact, during the Vietnam War his group focused on the innocent community caught in between the armies of the Communist and Democratic sides. Engaged Buddhist inspires us to practice the Dharma in ways that aid us in helping our communities become better stewards of the people and its resources (nature and otherwise) so that the collective suffering can be lessened. Hanh embraced this way of engaging the world as a form of following the natural conclusions of compassion combined with the reality of interconnection. In other words, monks and the layity can't practice compassion as called for by the reality of interdependence without being apart of the community.
Engaged was partly inspired by the Chinese monk Taixu. Taixu was concerned about monastics and laity alike in Pure Land Buddhism being distracted and obsessed with working to escape Earth for the otherworldly and supernatural Pure Land. He felt that the awareness of the suffering of others, which engenders compassion to help transform this current life--in this current moment into a happier reality was being lost out of a personal desire for transcendental bliss. It wasn't the belief in an end to suffering via Amida in the Pure Land itself that he was concerned about. It was with his perceived obsession that many had with it, which he felt was disconnecting people from each other, turning people into selfish beings and ultimately preventing the betterment of the society he lived in. It certainly inhibits one from fulfilling the Bodhisattva Vow taught by many Buddhist traditions.
At it's core, the Bodhisattva Vow is a commitment one makes to take action toward helping others within one's community receive the same respect, happiness and betterment that we might have and wish for our own family. This then is a wonderful code for politicians and other leaders today to guide their service for citizens. It goes to show that Buddhist principles aren't simply for spiritual pursuits but can also be beneficial in the public service arena. Still, I think it's important to find the middle ground between politics and spirituality. However, I feel that this decision to outright prevent monks and nuns in Bhutan from voting to be veering off the Buddha's compass of the middle path of finding a healthy balance between politics and spirituality.
Some believe that politicians are incapable of ruling in a just way as politics is driven by desire. Yet, take the example of Emperor Ashoka who used the Dharma as his guide when ruling his people. He was initially a brutal and greedy leader until he was changed by the Dharma, which led him to change many of his ways; including turning toward a vegetarian diet out of compassion for animals. His later rule was motivated by kindness, egalitarianism and philanthropy.
In Bhutan, the monks and nuns may personally decide to avoid politics altogether to dedicate all of their efforts toward spiritual endeavors. However, to prevent them from voting, (if they are so inclined) means taking away peoples' personal freedom, which isn't just antithetical to good government but also to the Dharma's message to not spread suffering and discord. It makes me wonder what the Dalai Lama would think of Bhutan's actions given his views on politics. As well as the reality that Bhutan predominately follows the Tibetan version of Buddhism. Preventing monks and nuns from voting means taking away from communities the many voices of moderation, peace, compassion and happiness that the monastics represent. If we feel that hearing their opinions helps improve life then we'd be silly to prevent those opinions from being registered in the political process.
At the same time, there does need to be a clear line drawn to prevent religion from getting involved in the actual crafting of policy in government. This also goes for preventing government from sanctioning and propagating one religion over another, which raises another question in Bhutan. The Bhutanese constitution that was drafted in 2008 still heavily favors Buddhism, which seems to contradict the government's policy of keeping religion and government separate.