If Matthew 5:13 says that disciples are salt and this means that because they have encountered Jesus and been fundamentally changed they are worthless to the world, what does Matthew 5:14–16 mean?
In Matthew 5:14–16, disciples are called light, and they are called to let that light shine so that people will glorify God. Verses 14–16 seem to imply that some people will in fact receive the disciples well and glorify God because of them.
You could then read Matthew 5:13–16 as a sort of two-ways text. The four verses would serve as an explanation and final consolation following on the heels of the beatitudes.
The beatitudes end with a difficult to receive promise of suffering for disciples. Verses 13–16, then, explain that it isn’t all bad. Jesus’ disciples will, quite naturally, be trampled by some people (ὑπὸ τῶν ἀνθρώπων, v.13). Disciples should, nevertheless, let their light shine before people (ἔμπροσθεν τῶν ἀνθρώπων, v. 16) because some will receive them well and glorify God. The verses are tied together by the fact that they both concern how people (ἄνθρωποι) receive Jesus’ disciples.
There are two ways: One leads to death (5:13). Many walk this path, and their footsteps echo the sounds of the martyrs crying out, “How long?!” The other way leads to life (5:14–16). Few walk this path, but if you get close enough to it you hear the songs of the saints singing the praises of the Father, Son, and Spirit.