Would you support the same thing done by, say, Christian bakers not providing a customer for religious-ideological reason?

I'll bite - but first some caveats.

I didn't follow the case and I'm only tangentially aware of it, I don't know who said what to whom and to how any of it is handled. I can't say with 100% certainty knowing the full explanation of the case that I would side with either the Christian bakers or the customer.

However though, it should be within a business owners right to deny someone access to a paid service or good on essentially any grounds.

Even if that business receives public benefits (directly or otherwise)?

Homosexuals pay taxes for streets and cops and electricity, under threat of violence.

Using those taxpayer services to then deny some taxpayers the same service you provide others is the functioeconomical equivalent of slavery.

Only if it's directly receiving government funds or dealing on behalf of the government should there be any restriction on whom they serve. Most businesses don't directly receive government funds.

For example, it should be illegal for a charter school to refuse to accept a gay student because they receive funding directly from the government. Same with a vehicle emissions test business that provides registrations. Or a hospital that has an emergency room.

Every business gets some amount of benefit from government services, but that isn't the same as it being funded by or operating in behalf of government.

The baker can shun the gay couple, the Nazis can spend their time and angst declaring under a cover of "Free speech is a human right" that all other ethno-religious groups are sub-human and unworthy of rights, and a reasonable human can decide to shun them both as utterly ridiculous.

If that reasonable human runs an open source app store, more power to them.

Intolerance of intolerance promotes tolerance, and F-Droid isn't the US government.

Being a nazi isn't a protected class.