Here is a question that is often asked. Can I run hydraulic lifters on a solid camshaft or can I run solid lifters on a hydraulic camshaft? The most common reply is why do you want to do that? Answering a question with a question does not really answer the original question. I will try to give a better answer. It is not a short answer. Unfortunately I am not a teacher and do not possess the skills needed to communicate knowledge. I can only try and explain.
When a cam profile is designed, it is either designed for a solid tappet or a hydraulic tappet. Not both. The differences in the two designs are the profile ramps. You can think of the profile ramps as motorcycle jumping ramps. The ramps play a very important role in how the motorcycle takes off and lands during the jump. There is a launch ramp and a landing ramp. On the cam profiles there is an opening ramp and a closing ramp. A hydraulic profile ramp is designed for zero lash. Meaning that the valve train components are in constant contact with each other. When the lobe rotates, the tappet will follow the cam profile and will immediately exert force on the valve train. Since there is no lash to take up, the hydraulic ramp is short and will start to open the valve soon in the rotation of the lobe. Even though the hydraulic ramp is short, it is designed so not to exert too much force too quickly on the tappet and push oil out of the hydraulic unit. The initial opening is slow and gentle compared to the solid profile ramp.
The solid profile ramp can initially open the valve quicker once the lash is taken up. This extra length designed in the ramp to take up the lash obviously makes it a longer ramp than the hydraulic one. If a hydraulic tappet is run on the solid ramp the valve will start to open on this part of the ramp causing the valve to open sooner and stay open longer than what was intended. This of course changes the valve timing. How much the valve timing changes will depend on the actual design of the ramp. This is where the problem lies. If you don't have the cam profile design, that makes it hard to answer the original question. The valve lift will also be higher since there is no lash. That could be a potential piston to valve clearance problem or some other mechanical interference.
Running a solid tappet on a hydraulic camshaft is a little more involved. You must decide what to adjust the lash at. The hydraulic ramp was designed for zero lash, but using the solid lifter will introduce lash. Ideally you want to adjust the lash as close to zero as possible. This will keep the valve timing close to what it was with the hydraulic tappet. The more lash you run the more you will change the valve timing. Obviously controlling the valve timing is the main purpose of the camshaft and determines how the camshaft performs.
Basically the same explanation applies to the closing ramps. There is not any logical reason to run tappets on the wrong ramp design. Using the proper camshaft with the correct cam profile designs will always perform better.