Yes it is asking for opinions, which i will investigate further on my own. opinions would be helpful in this particular circumstance.
In their Study of SGI, Phillip Hammond and David Machacek suggest that the religion is "characterized by an almost libertarian perspective on individual behaviour."
I visited some SGI meetings many years ago, and those I met seemed like nice enough people, OTOH I didn't understand (didn't get much of) their doctrine.
They call themselves Buddhist, e.g. here is the meta description from their web site,
<meta name="description" content="Worldwide Buddhist network which promotes peace, culture and education through personal transformation and social contribution. Buddhist concepts, news, links with SGI organizations around the world and more." />
Wikipedia's introductory paragraph says,
Soka Gakkai (Japanese: 創価学会?) is a Japanese new religious movement based on the writings of Nichiren and the teachings of the organization’s presidents Tsunesaburō Makiguchi, Jōsei Toda and Daisaku Ikeda. It is one of the larger Japanese new religions. Originally a lay group within the Nichiren Shōshū Buddhist sect, the Gakkai reveres the Lotus Sutra and places the chanting of the name of the Sutra at the center of devotional practice. The movement is publicly involved in peace activism, education and politics. It has also been at the center of controversies.
I'm not sure whether to say it is a Buddhist tradition or whether it's from a Buddhist tradition. Here's what they write about their organization:
Soka Gakkai International (SGI) is a lay Buddhist movement linking more than 12 million people around the world. SGI members integrate their Buddhist practice into their daily lives, following the Lotus Sutra based teachings of Nichiren, a 13th-century Japanese Buddhist priest.
Just as the lotus blooms in a muddy pond, all people can manifest the Buddha nature--inner resources of courage, wisdom and compassion that can equip them to overcome life's challenges and lead happy and fulfilling lives. As "engaged Buddhists," SGI members aim to create value in any circumstances and contribute to the well-being of others. Their practice sparks a process of ongoing inner transformation and empowerment known as "human revolution." The promotion of peace, culture and education is central to SGI's activities.
I have been to 3 Buddhist centres/traditions: Theravada, Tibetan Buddhist and New Kadampa Tradition.
Based on what I have seen I would say New Kadampa was the most liberal as they claim to have "a modern Buddhism for a modern world", however I choosed to go with Theravada for many reasons, I recommend you to investigate and do not choose a tradition based on who is more liberal, remember the Buddha's teachings were not about being liberal, but refraining from many things.
It is important to mention that Zen Buddhism is also known for being liberal when compared to other traditions, but I cannot confirm it as I have never checked it for myself.
If you mean liberal in the sense of non-traditional or neo-traditional the most accommodating of the modern way of life, I would look to outgrowths in the US because I am most familiar with that. Some sects practice freely to many degrees with women and men together such as Trungpa.
For instance Roshi Suzuki wrote the following: http://www.arvindguptatoys.com/arvindgupta/zenmind.pdf
It is a very mild manner zen book. It has guidelines but not ones made of concrete, but ones that are flexible.
There are a number of liberal teachers that may be of interest. Each person must examine their own beliefs and find a path that works for them. Someones tame philosophy could be another's abomination.
This list is recommended reading. You may choose freely from this list and make up your own mind how you define liberal.