How much thrust is lost due to the bleed air system?
For the Boeing 737-800:
Bleeds off:

If bleed air is turned off, it gives ~1% N1 increase. This higher N1 also means a 1 or 2 knot faster $V_1$ and/or $V_{mcg}$. Bleeds on adds about a 2.5-tonne correction to the gross weight.

For the various anti-ice:

The penalty can be as high as 5% N1. Note the single- and dual-sources figures. Dual means APU is running and is providing bleed air.
Exact loss in thrust (force)
That will be very hard to calculate without test bed data from the engine maker. Not to mention it varies with the different elements: pressure altitude, temperature, forward speed, etc. That's why I included the V1 and weight impacts.
Based on the graph below, 1% N1 at high takeoff power equates to about 2.4% of total thrust. That should be treated as a ballpark figure.
(Source)
In cruise however, having all anti-ice on might warrant flying lower due to the decreased thrust.
Other uses and alternatives
Bleed air used for cooling the turbine blades for example, helps increase thrust, not decrease, as the burners can run hotter without damaging the turbines.
The &quot;all-electric&quot; Boeing 787 uses bleed air for engine anti-ice. Using the generator to run the other anti-ice elements also reduces the thrust due to the shaft off-take. But, there is the benefit of weight reduction.