From What are the most common damage types per spell level?, there are 14 spells that deal radiant damage, making it the 5th most common spell damage type. These are predominately cleric and paladin spells. There is at least one for every spell level except 7th and 9th so they are available early and often. Radiant damage is a good choice because few creatures are resistant or immune to this type of damage unlike, say, fire which is both the most common spell damage type and the most resisted.
That said, your question is highly dependent on how you use undead in your game. If the players never fight them then obviously it will have no effect whatsoever. If the campaign is a zombie apocalypse and that's all they fight then it will have a much greater effect. How much you telegraph what they will be facing will also be a big factor - clerics and paladins with foreknowledge can optimise their spell selection. If this telegraphing extends to pre-character creation then players may be drawn to paladin and light-domain clerics, this is not necessarily a bad thing.
As to the effect of vulnerability on CR the DMG has this to say (p. 277):
Vulnerabilities don't significantly affect a monster's challenge rating, unless a monster has vulnerabilities to multiple damage types that are prevalent, especially bludgeoning, piercing, and slashing.
This makes sense, if 1 (or 2) PCs in a party of 4 do double damage on a successful hit the effect is as if there was 1 (or 2) more PCs making attacks but there are still only 4 copping damage. The creatures will be down 1/4 to 1/2 as quick but most creatures hand out the bulk of their damage in the first couple of rounds anyway.
Of course, you are the DM, if you slip 1 more zombie into the pack or give the lich 25% more hp the effect of radiant vulnerability will be effectively cancelled out but the PC who picked paladin still gets to feel clever.