If your undersink trap and drain connections are clean and well-designed, and if you are not just clogging your garbage grinder, then your back-ups are due to some sluggishness of drainage further down. This sluggishness can come from only three sources: 1) clogged drainpipes; 2) poor drainpipe sizing and/or slope (including “bent” drainlines; and, 3) inadequate or clogged venting.
Be careful what you put down the kitchen sink. Grease has a way of clogging drains. My disdain for garbage disposals is no secret on this board. They tend to give homeowners a false sense that it’s OK to use their kitchen sinks as garbage cans, that it’s perfectly OK to dump chicken bones and potato peels down the drain rather than in the garbage can…
Fortunately you can fit a standard removable drain strainer over the garbage disposal drain opening, and you can empty that strainer into a conveniently situated garbage can under the sink.
If we ever take a vote to elect the most foolish plumbing invention of the past 100 years, I would nominate the garbage disposal.