Note that the GATK programming framework (engine, infrastructure and utility tools) remains fully open source under the MIT license. Developers are free to write their own tools on top of the GATK and distribute them without any restrictions. Only a subset of analysis tools are actually covered by the license restrictions.
GATK is a pretty big toolset, so it's hard to replace all of it in one fell swoop. But as far as variant-calling goes, you can use BBMap's "callvariants.sh" to get better results (from my tests) in a tiny fraction of the time. The BBMap package is fully open-source.
It's also easy to use - "callvariants.sh in=mapped.sam out=vars.vcf ref=ref.fa ploidy=2". I wrote it partly because alternatives were just too slow to seriously consider as part of a high-performance pipeline, and partly because they yielded incorrect results. I needed a fast program that gave correct variant calls and there just weren't any, so I wrote one myself.