The thing about no beans in chili is that beans release a chemical while cooking that causes the chili meat clumps to fall apart and the chili becomes soupy and runny.
As long as you confine your perversion to your own bowl, it's OK to put beans in chili. In other words, use a separate pot to cook the beans, use separate utensils than are used for the chili, mix your beans in at the table rather than at the stove, then it's OK. Even the most ardent chilihed will likely let you off with a little (more or less) gentle teasing. You're only in actual physical danger if you should attempt to sneak your beans into the main chili pot and so mess things up for everyone else.
But there's plenty 'nuff beans in Tex-Mex cuisine anyway, pintos, black beans, boracchos, etc. One meal without beans won't hurt you.
I speak of course about real Texas chili, not the various stews, soups, porridges, sopas, caldos, and pastas that people who've never seen a ristra sometimes label chili - despite having no chili peppers a'tall in them!