Left handedness has long been stigmatised in many societies, coming to be superstitiously associated with various negative characteristics. This is analogous to stigmatisation of other relatively uncommon phenomena in people which contrast how the 'normal' majority act or look e.g. albinism, dwarfism:
Many languages still contain references to left-handedness to convey awkwardness, dishonesty, stupidity, or other undesirable qualities. Even in relatively advanced societies, left-handed people were historically (and in some cases still are) forced as children to use their right hands for tasks which they would naturally perform with the left, such as eating or writing.
This prejudice has bled into a number of expressions in many languages, including Spanish:
- Cuando alguien hace algo fuera de la ley o de la moral, suele hacerlo… por la izquierda
- Si tienes un mal día es porque te has levantado… con el pie izquierdo o por el lado izquierdo de la cama.
- Una persona que no sirve para nada… es un cero a la izquierda.
- Al que no sabe bailar le dicen que tiene… dos pies izquierdos.
- Las aves que anuncian malos agüeros decimos que vienen… por la izquierda.
The word siniestro itself has been displaced by izquierda, zurdo due to the taboo nature of the word.
Due to these negative historical associations, lefthandedness itself has come to be used in many expressions as a euphemism for other perceived negative characteristics which differ from 'the norm'. One example is, as you note, being gay:
In 19th-century Europe, homosexuals were referred to as "left-handed".
This connotation is visible today in the English phrase "batting lefty", as well as the South American Spanish use of zurdo.