Can Neon tetra Live With Rummy-nose tetra?

Temperature is the whole of the problem. The rummy nose wants 24 to 27 °C and the neon 21 to 25, which leaves 24 to 25 °C as the only ground they share. That is workable but it leaves no margin: set the heater at 24.5 and a warm room in summer pushes the neons past their ceiling.

Nothing else objects. Both are very peaceful, the rummy nose is recommended alongside other characins, and their pH ranges meet comfortably at 5.5 to 7.

Both need numbers, the rummy nose more than most. It is one of the more tightly shoaling small tetras and does badly in insufficient numbers, so buy at least 10 and preferably more, with 8 to 10 neons beside them. Two schools of that size call for the rummy nose's 80 litres rather than the 54 a single school needs. If you cannot hold the temperature steady, keep one species and choose a second that overlaps it properly.