1. a UBI would very likely be unconditional and universal (as long as you are a citizen) so relying on it would carry no social stigma, because everybody gets it.
2. you still get a UBI if you get yourself a job – which means a job gives you extra money. With most current unemployment benefits you could sometimes loose money when you get a job, or you'd just get a tiny bit extra for a lot more work (especially if you are doing demanding physical labour).
This means the incentives are completely and utterly different – and incentives kinda matter when we want to discuss human behaviour.
Essentially then, you have the same idea you have today: those who will rely on UBI are the same people who rely on social benefits today, and those who do not get it are the ones who will have to fund it (with a slightly enlarged soft border between the two). The stigma isn't because people know that you get social benefits (the records aren't public), it's that they don't see you working.
The cut-offs are an issue, but we already have Mini (up to 450€) and Midi Jobs (up to 1300€) where you'll not get any reduction in benefits for 100€ and 20% of whatever you make on top will also not affect your benefits. That's not a perfectly soft threshold, but it's not a hard cut-off either. The thresholds that you lose money at are much higher (e.g. earning just a little bit too much to be eligible for subsidized housing, which is close to the median salary in most states).
As for the stigma associated with not working: true, but it's not part of, or encouraged by, the law. It will be the same with UBI, it will not be admired to not contribute to society. Some people may feel that they do in fact contribute, but society at large values other things than self-actualization.
The university/higher education system is weird, but for other reasons (my personal theory is that you can't have organized bureaucracy in Germany without some senseless cruelty). It's another point on the board for "free doesn't necessarily give you the expected results" though: unlike in the US, it's free, our "student loans" (Bafög) are generally interest free and 50% of the amount owed will generally be forgiven. Obviously, we see plenty of people entering, but we don't see the results you'd imagine if costs were what's holding people back.