That's about as much support for Google as if I bought a product from a storefront that's in a building owned by a landlord who supports a cause I don't agree with. First of all, I (as a consumer) would have no idea who owned that building, and secondly the link between my purchase and money flowing to that unsavory cause is so far removed that it's not even worth considering.

Go far enough down any business transaction and you'll find a cause you disagree with. If the tree you planted makes oxygen for your worst enemy, will you cut down the tree to spite them?

My understanding is that Firebase is free. However, even if it wasn't I still think the link is tenuous to the point of meaningless. Spending attention on HN does not make google any richer, it stretches the definition of the word "support" in a way that misses the point within the context of boycotting a company. If every HN reader quit the site today only a Firebase SRE would take notice, if every HN reader quit using Gmail it'd cost google a considerable amount of money.