Well that is exactly the point. Of course, climate activists reducing their individual leisure demand would decrease global carbon emissions only insignificantly, if at all.
That's not the point here. The point is that climate activists ask their government for big changes because they fear civilization could end otherwise. And those big changes would have significant impact on the lifestyle of almost all people affected by these laws. So, why should one be willing to (and thus, vote for the changes) change ones lifestyle, if the advocates just say "well, I stop travelling abroad, when everyone else stops as well (and other carbon emission is reduced, too)"? The OP is about credibility, or, even lower level: sympathy.
Maybe it becomes more obvious if we look at one specific example. In the Netherlands they lowered maximum speed on highways to 100 km/h (from 120 km/h). Correct me if I'm wrong but the carbon saving from that law is close to non-existent compared to the whole economy's carbon emissions.
Or, the whole EU banned light bulbs. Also, the energy saving compared to the whole EU's energy consumption is probably sub 1%. And with the advent of white LEDs, people just use more light and the overall effect is even less.
Both measurments combined have an impact less than your claimed 5%-10%. Does that mean that government should stop taking small steps, and only the "big shot" counts?
Or can small steps (by governments OR individuals) be a tool to increase awareness?