Are there tabletop RPGs where magic and technology really clash?

Look for rules that make the conflict matter during play, not just in the setting. For example, technology might work reliably where magic is disrupted, while powerful magic might bend the rules that technology depends on. Both sides should still have things they can do well, so interference creates choices rather than shutting someone out.

A flexible system could handle this if it lets you define clear limits and interactions. Decide what conditions weaken magic, what can disrupt technology, and what each approach can accomplish that the other can't. Make those effects predictable enough for players to plan around, and give non-casters their own strengths instead of treating them as weaker versions of spellcasters.