Custom firmware 3.10 OE-A (a mix of 1.50 and 3.10 mix as one) supports homebrew without GTA, you just load it from the memory stick in the GAME menu, along with PS1 games. It's by far better than 1.50 as it also has a recovery menu if you semi-brick.
It's just Sony's official firmware version 3.10 (just plain 3.10, not mixed with 1.50) that won't let you use hombrew, even via GTA they won't work as the save data exploit is patched up.
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