Qt is entirely and certainly FOSS. Pick your license: GPL or LGPL at your choice.
Anything and everything in Qt that an application developer can use, definitely. Everything Qt installed in Linux distributions is available under FOSS licenses.
However, there is one or two Qt packages that are not licensed under FOSS licenses, and not available in standard Linux distributions. The main one is
Qt for MCUs, which is only available under a commercial or an evaluation license.
I've talked about this in a different thread, but I'll repeat the core points: One can create proprietary Qt applications based on the LPGL license. One will not be required to expose their own source code. Open source applications can use the GPL license, proprietary applications the LGPL license (if they link dynamically to the Qt libraries). The commercial license gives you commercial support.
Satisfying the Qt developer community, and the Qt company, is easy: be proud of using Qt in your application, link to qt.io for further information, and abide by the license. If you compile your own distributable Qt binaries, be open about the exact toolchain (including compiler version and library configuration); optimally, you'd provide build scripts that builds them for each target OS and architecture when run in a directory containing the pristine upstream sources. If you do modify any of the Qt sources, you do need to provide your customers with the modified Qt sources too.
In short: the language at the web pages may seem scary to those used to very friendly FOSS projects, but that's just marketing. Everything behind that is quite friendly to FOSS developers. And if you are a developer relying on the LGPL license, they aren't hostile, just indifferent: you neither hurt nor help. (But, if you do stuff I mentioned above, you actually do help a bit, at least as an example of doing things
right as a completely outside party.)
If you say that software that's opensource and released under the GPL and/or LGPL isn't FOSS,
then many software will not be FOSS like for example the GTK toolkit.
The fact proprietary non-FOSS closed-source applications and libraries are explicitly allowed to dynamically link to any LGPL-licensed library/toolkit/framework, can be confusing to those who do not understand the core idea of FOSS: it is not about zero price, it is about end-user freedom.
Even the dynamic linking requirement is really about end users: they must be able to recompile or create their own variants of those LGPL-licensed libraries, so that they can have the proprietary non-FOSS application run with those modified/different libraries.
This is the reason why so many of the core libraries are LGPL-licensed. (I do not consider LGPL to be a "compromise" that for example the
Wikipedia LGPL article claims, because LGPL fits perfectly well within the
free software philosophy: it is about personal, end-user freedom. After all, it initially wasn't "Lesser GPL", it was "Library GPL". It's just that it depends on the exact library what license is best suited; not all libraries need to or are best licensed under LGPL.)