A 1:2 splitter typically has 3.5 dB of insertion loss. That is, just by putting a splitter in front of your DOCSIS modem, you cut your DOCSIS signal in half.
Decreasing your DOCSIS signal is not a problem if it still ends up within the ideal range of 0 dBmV ±7. But if it was already near the weak edge of that range, say at -6 dBmV, subtracting another 3.5 dB of signal would knock the signal down to -9.5 dBmV, which is outside of the acceptable range, and could cause an increase of symbol errors, including uncorrectable errors.
(Well, to be fair, some people think 0dBmV ±10 is an acceptable range, but whatever range is acceptable, adding that splitter may have knocked you out the bottom of the acceptable range.)
You should log into the settings page of your DOCSIS device and look at its status / statistics / diagnostics for its DOCSIS interface. Look at the signal levels for all the downstream channels and make sure they're all within the 0 dBmV ±7 range, hopefully centered around 0 dBmV.
If adding that splitter did knock some of your channels down below -7 dBmV, you might need to contact your ISP to increase the signal they're sending down the line to your house. This is a routine part of DOCSIS coax network maintenance.
If you want to try to avoid making your ISP roll a truck to fix your signal levels, map out and inspect the coax splitter tree on your premises. Remove all unnecessary splitters. Make sure all splitters are MoCA-rated. If you have any splitters with unused output legs, replace them with smaller splitters. For example, a 1:4 splitter, internally, is like a tree/cascade of three 1:2 splitters, so a 1:4 splitter has 7 dB of insertion loss. If you only need a 1:2 splitter there, you can get back 3.5 dB of signal by replacing the 1:4 with a 1:2.
(By the way, since you're using MoCA, be sure to install a MoCA point-of-entry filter between the coax line from the ISP and the first splitter on your premises. A MoCA point-of-entry filter helps MoCA signals traverse your coax splitters, improving MoCA performance. It also keeps your MoCA signals from leaking onto your ISP's network, or into your neighbors homes. Also be sure to set a strong password for your MoCA network; don't just rely the point-of-entry filter for security.)