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The problem is: what does it mean to do that? Right now, we don't have an organized revolution or movement. There needs to be a specific call to action. If you want people to "give up the comforts" of their lives, they need to know what doing that will accomplish, what the specific goal of the movement is, and how "giving up the comforts" will help to achieve it.
What you might actually be asking is for people to risk their jobs by going on general strike, their homes by not paying rent, etc. This is really more than "the comforts of their lives", it is their ability to survive and feed their families.
The other problem is, any cause that only requires people to "give up the comforts of their lives" likely won't be highly impactful. For instance, general strike and protest might help the climate crisis, but giving up plastic straws and driving less or whatever really won't make much of a dent compared to the massive impacts of global capitalism.
Driving less would make a huge impact, around 45% of all transport related emissions are from passenger traffic, that's buses, taxis, and most of all regular people driving their cars. Transport related emissions accounts for 24% of global emissions, so just passenger traffic is almost 11% of global emissions. Everyone hates aviation, but that's "only" around 3% of global emissions, shipping also around 3%, and road freight is 7%.
Source: https://ourworldindata.org/co2-emissions-from-transport
That is a fair point. My only counterargument would be that due to the way cities are set up, a large portion of those emissions come from commuting. The reason people commute is they have to earn money to pay bills so they can feed their kids and keep a roof over their heads.
So, asking people to drive less could mean asking them to give up their employment, which could be much more than "giving up the comforts of their lives" like the OP suggested - again, it could really put their livelihoods in jeopardy. And, without an organized cause, clear goal, a call to action, and clear communication about why their specific sacrifices are necessary, people will not take such huge risks.