Most of the BPSK waveform examples in text books/online are for carrier frequencies that are integer multiples of the bit rate. This means that when the symbol polarity changes there is a discontinuity in the waveform - but it doesn't jump signal level, it just heads the other way. When the carrier frequency is not an integer multiple, the waveform does need to jump instantly from one signal level to another (ie the symbol change takes place when the signal level is not at signal level 0).. Does this increase required bandwidth or have any other undesirable effects??
The examples in the textbook are chosen for clarity. They will have like what, a 2:1 ratio between carrier and data frequency? In practice this may be 10 000:1 or more. And even with the carrier being an exact multiple you can't be sure of the phase; chances that zero crossings of carrier and data coincide are slim.
You need a higher bandwidth to get the sudden changes in level right, but if you have 10 000 carrier sines for 1 bit you don't care about that distortion in the first sine.
I wouldn't worry about it.
Any jump in the time domain has a very wide bandwidth in the frequency domain (theoretically infinite). So an encoding that has jumps usually needs to be lowpass or bandpass filtered (or will be by the channel). Thus the received signal won't have the discontinuity, but some smoothed (filtered) interpolation for some transition time (with a duration depending on the narrowness of the filter). Decoding can be slightly complicated in that it has to ignore or compensate for this periodic waveform distortion, compared with phase synchronous modulation. But that's usually done as a normal part of the decoding process.